text:
\section{Introduction}
\par

The AdS/CFT correspondence\cite{Maldacena:1997re} implies that the phases of string theory can be studied by studying those of the dual gauge theory(\cite{Gubser:1998bc,Witten:1998zw,Witten:1998qj}). In the case of type $IIB$ string theory in $AdS^{5}\times S^{5}$ the phases can be studied using the large N limit of a unitary matrix model(\cite{Sundborg:1999ue,Polyakov:2001af,Aharony:2003sx,Liu:2004vy})\footnote{Phases of large N gauge theory is also discussed in \cite{Hallin:1998km,Schnitzer:2004qt}}. The unitary matrix is the finite temperature Polyakov loop which does not depend on the points of $S^3$. This fortunate circumstance is due to the fact that in the Hamiltonian formulation, N=4 SYM theory at a given time slice, is defined on the compact space $S^3$ and the $SO(6)$ scalars are massive because of their coupling to the curvature of $S^3$. These facts imply that, in principal, one can integrate out almost all the fields and obtain an effective theory of the zero mode of the gauge potential $A_0$.

Using this method a detailed correspondence of the critical points of the gauge theory effective lagrangian and the critical points of supergravity (discussed by Hawking and Page\cite{Hawking:1982dh}) can be constructed at the leading order of the $1/N$ expansion. These are $AdS_5$ and the small and big black holes (as \cite{Alvarez-Gaume:2005fv}  we refer to these as SSB and BBH.) It turns out that in the gauge theory these critical points are in the gaped phase, where the density of eigenvalues vanishes in a finite arc of the circle around which the eigenvalues are distributed. The closing of the gap, corresponds to the Gross-Witten(GW) phase transition(\cite{Gross:1980he,Wadia:1979vk,Wadia:1980cp}). In a window around this transition, the supergravity description of string theory is likely to smoothly cross over into a description in terms of heavy string modes. \footnote{In \cite{Alvarez-Gaume:2005fv}, besides the vicinity of the Gross-Witten transition, authors also studied $1/N$ corrections and presented formulas for the partition function in the vicinity of blackhole nucleation and the Hagedorn transition.}

In this paper we extend the discussion of the correspondence between R-charged $AdS_{5}$ blackholes(\cite{Cvet1,Cvet2,Chamblin:1999tk,Chamblin:1999hg,Hawking:1999dp}), and the effective unitary matrix model(\cite{Gross:1980he,Wadia:1979vk,Wadia:1980cp,Halpern:1982rd}). R-charged black holes are known to have a rich phase structure in the canonical and grand canonical ensemble. In the canonical ensemble the fixed charge constraint, contributes an additional logarithmic term $\log(TrUTrU^{\dagger})$  involving the order parameter, to the gauge theory effective action. This term is crucial for matching with supergravity. We analyze the implications of this term in the large N limit and compare with the various supergravity properties like the existence of only blackhole solutions in the canonical ensemble and also the existence of a point of cusp-catastrophe in the phase diagram.

\par
The plan of this paper is as follows. In section \ref{Supergravity} we give a brief review of charged $AdS_5$ blackholes. In section \ref{sec:free} and section \ref{sec:small} we discuss the effective action of the gauge theory at zero and small coupling, in the fixed charged sector. At zero coupling there is exactly one saddle point and the value of $TrUTrU^{-1}$ at the saddle point is always non-zero. For a small positive coupling there are two stable and one unstable saddle points, all with a non-zero value of $TrUTrU^{-1}$. They merge at the $GW$ point. In section (\ref{sec:simmod}) we discuss the model effective action at strong coupling. Here too, there are three saddle points,two stable(I,III) and one unstable(II). In the region $\rho>\frac{1}{2}$, $I$ and $III$ can be identified with a stable small blackhole and stable big blackhole respectively. Saddle point $II$ is identified with the small unstable black hole. The merging of saddle points leads to critical phenomenon whose exponents can be calculated and shown to agree with supergravity. This is discussed in section \ref{Unin}. We have also calculated the $o(1)$ part of the partition function near the critical point.

\section{R-charged blackholes in $AdS_{5}$ and critical phenomena }\label{Supergravity}
The R-charged $AdS_{5}$ black hole and relevant phase structure were discussed by A.~Chamblin, R.~Emparan, C.~V.~Johnson and R.~C.~Myers (\cite{Chamblin:1999hg},\cite{Chamblin:1999tk}). Here we review their result. The Einstein--Maxwell--anti--deSitter (EMadS$_{n+1}$) action may be written as
\begin{equation}
I = -\frac{1}{16{\pi}G} \int_{M} d^{n+1}x \sqrt{-g} \left[\widetilde R - F^2 +
\frac{n(n-1)}{R^2}\right]\ ,
\label{actionjackson}
\end{equation}
where $\widetilde R$ is the Ricci scalar and $R$ is the characteristic length scale of $AdS$.
The metric of the Reissner--Nordstr\"om--anti--deSitter (RNadS)
solution is given in static coordinates by

\begin{equation}
ds^2 = -(1 - \frac{m}{r^{n-2}} + \frac{q^2}{r^{2n-4}} + \frac{r^2}{R^2}\ )dt^2 + \frac{dr^2}{1 - \frac{m}{r^{n-2}} + \frac{q^2}{r^{2n-4}} + \frac{r^2}{R^2}\ } +r^{2}d{\Omega}^2_{n-1}\ ,
\label{BlackHole}
\end{equation}
\noindent
The parameter
$q$ is proportional to the charge
\begin{equation}
Q=\sqrt{2(n-1)(n-2)}\left({\omega_{n-1}\over 8\pi G}\right)q\
\label{thecharge}
\end{equation}
 and $m$ is proportional to the ADM mass $M$ of the blackhole.
\begin{equation}
M={(n-1)\omega_{n-1}\over 16\pi G}m\
\end{equation}
$\omega_{n-1}$ is the volume of the unit $(n{-}1)$--sphere, and the gauge potential is given by
\begin{equation}
A_{0}=\left(-{1\over {\sqrt{2(n-2)\over n-1} }}{q\over r^{n-2}}+\Phi\right)
\label{pure}
\end{equation}
where $\Phi$ is the electrostatic potential difference between the black hole horizon and infinity.
\par
For n=4 the solution (\ref{BlackHole}) can be considered as a rotating black hole in $AdS_{5}\times S^{5}$ with angular momentum in the internal space $S^{5}$.\footnote{The EMadS system described here may be thought as the dimensional reduction of $AdS_{5}\times S^{5}$ to $AdS_5$. Generally introducing angular momentum in $S^{5}$ will distort $S^5$. This distortion is not taken into in the EMadS reduction \cite{Behr,Kraus:1998hv}. We thank S.Trivedi for pointing this out to us. However these details do not change our main consideration.} The symmetry group of $S^5$ is $SO(6)$ and the black hole we are discussing has equal $U(1)$ charges for all the three commuting $U(1)$ subgroups of $SO(6)$, the  R-symmetry group of the $N=4$ $SYM$. Hence we are dealing with a system which has the same chemical potential $\mu$ for all three $U(1)$ charges in the grand canonical ensemble or equivalently three fixed equal U(1) charges in the canonical ensemble.

\subsection{Equation of state}\label{sec:state}

In order to discuss the thermodynamics, we consider the Euclidean continuation ($t{\to}i\tau$) of the solution, and identify the imaginary time period $\beta$ with the inverse temperature. Using the formula for the period, $\beta{=}{4\pi}/{V^{\prime}(r_{+})}$ (for a review see \cite{David:2002wn}), we get

\begin{equation}
\label{betaform}
\beta = \frac{4{\pi}l^{2}r_{+}^{2n-3}}{nr_{+}^{2n-2} +
(n-2)l^{2}r_{+}^{2n-4} - (n-2)q^{2}l^{2}}\ .
\end{equation}

\noindent This may be rewritten in terms of the potential as:
\begin{equation}
\beta = \frac{4{\pi}l^{2}r_+}{(n-2)l^{2}(1-c^2\Phi^2)+nr_+^2}\ .
\label{betaformtwo}
\end{equation}

The condition for euclidean regularity used to derive (\ref{betaform}) is equivalent to the condition that the black hole is in thermodynamical equilibrium. The equation (\ref{betaform}) may therefore be written as an equation of state $T{=}T(\Phi,Q)$. From this equation of state we see that for fixed $\Phi$ we get two branches, one for each sign, when the discriminant under the square root is positive\cite{Chamblin:1999hg}. For fixed $Q$, $T(\Phi)$ has three branches for $Q{<}Q_{crit}$ (Let us call them $I$, $II$, $III$) and one for $Q{>}Q_{crit}$. The critical charge is determined at the "point of inflection'' by $\left(\partial Q/\partial\Phi\right)_T{=}\left(\partial^2 Q/\partial\Phi^2\right)_T{=}0.$

\par
 The qualitative features of $\beta(r_+)$ for varying $q$ are shown in
Fig \ref{fig:beta}.
\begin{figure}[h!]
\begin{center}
\includegraphics[height=2in]{beta.ps}
\end{center}
\caption{Plot of $\beta(r_{+})$ for q increasing from the left. The third graph from the left is for $q_{crit}$ }
\label{fig:beta}
\end{figure}
There is a critical charge, $q_{\rm crit}$, below which there are three solutions for $r_+$ for a range of values of $T$,
corresponding to small ($I$), unstable($II$), and large ($III$) black holes. For fixed $q<q_{crit}$ only branch $I$ is available at low temperatures. At $T=T_{02}(q)$, there is a nucleation of two new solutions, $II$ the unstable small black hole solution, and $III$ the stable big black hole solution. As the temperature is increased further, the black hole $II$ approaches black hole $I$ and at $T=T_{02}(q)$ the two solutions merge.
\par
  As $q$ is increased further, $T_{02}$ increases, whereas $T_{01}$ decreases. At $q=q_{crit}$ we have $T_{crit}=T_{01}=T_{02}$. At $q_{crit}$ and $T_{crit}$ all three solutions merge. In the language of catastrophe theory this is a cusp catastrophe. As we increase $q$ beyond $q_{crit}$ there will be just one solution for all temperatures $T$.
\par
 We wish to take note of some properties of the phase diagram.

\begin{enumerate}
\item Thermal $AdS$ is not a solution and all three branches of the solution represent black holes.
\item There exists a critical point where the three solutions of the system merge. It is a point of fold catastrophe.
\end{enumerate}

\subsection{Critical Phenomena}
\par
 The critical point ($Q_{cit}$,$T_{crit}$) may be approached from various directions in the parameter space. If we set $T=T_{crit}$, then the equation determining $(r-r_{crit})$ takes the form ($r_{crit}$ is the radius of the critical black hole)
\begin{eqnarray}
(r-r_{crit})^{3}= {\cal C} (Q-Q_{crit})
\end{eqnarray}
${\cal C}$ is a numerical constant. The critical exponent here is $\frac{1}{3}$, since
\begin{equation}
(r-r_{crit}) \propto (Q-Q_{crit})^{\frac{1}{3}}
\end{equation}
\par
 As discussed in \cite{Chamblin:1999hg} (Fig16), the critical point may also be approached through the coexistence line in the parameter space. The coexistence line is the line with the property
\begin{equation}
\nonumber S_{I}=S_{III}
\end{equation}
for the parametric range $q<q_{crit}$. It is the line where the Hawking-Page (first order) transition from the small black hole to the big black hole takes place. As we approach the critical point through this line, we have the relation
\begin{eqnarray}
(r_{I}-r_{II}) \propto (T-T_{crit})^{\frac{1}{2}}
\end{eqnarray}
 \par
In the following we will present an understanding of these properties. Before we do the matching with supergravity we would like to present a discussion of the gauge theory in the limit when $\lambda=g^2 N=0$ and also when $\lambda << 1$. In these cases we of course can not compare with supergravity which requires $\lambda >> 1$.

\section{Free YM theory}\label{sec:free}
\subsection{Effective action with chemical potential}
In this section we  briefly review (see \cite{Liu:2004vy},\cite{Aharony:2003sx}) the effective action for a
free $SU(N)$ Yang-Mills theory (with adjoint matter) on a compact manifold $\Im$ in the large $N$ limit. The basic idea is to integrate out all fields in the theory except for the zero mode of the Polyakov line. The partition function is then reduced to a single unitary matrix integral.

Expanding all fields in the gauge theory in terms of harmonics on $\Im$, the theory reduces to a zero dimensional problem of free $N \times N$ Hermitian matrices
 \begin{eqnarray}
{\cal L} = {1 \ov 2} \sum_a Tr \left[ (D_t M_n)^2  - \omega_n^2 M_n^2 \right]
\label{simlad}
\end{eqnarray}
The sum in (\ref{simlad}) )is over all field types and their Kaluza-Klein modes on $\Im$.
$\omega_n$ is the frequency of each mode. The covariant derivative in (\ref{simlad}) is
\begin{equation}
D_t M_n = \partial_t M_n - i [A_{0}, M_n]
\end{equation}
$A_{0}$ comes from the zero mode (i.e. the mode independent of
coordinates on $\Im$) of the time component of the gauge field and
is not dynamical. The partition function of the theory at finite temperature
can be written as a unitary matrix integral by integrating out all fields in (\ref{simlad}) except for $A_{0}$. Hence we have
 \begin{eqnarray}
 Z & = \int DU \, \prod_n
 \left({\rm det}_{adj} \left(1- \epsilon_n e^{-\beta \omega_n} U \right)\right)^{-\epsilon_n}
 \end{eqnarray}
where $U={\rm exp}(i\beta A_{0})$ is a $U(N)$. ${\rm det}_{adj}$ denotes the
determinant in the adjoint representation and $\epsilon_n =  1$ ($-1$)
for bosonic (fermionic) $M_n$. The above equation can be
 expressed as
 \begin{eqnarray}
 Z =  \int DU \, {\rm exp} (\sum_{n=1}^\infty {z_{n}(\beta) \over n})
 Tr U^n Tr U^{-n} )
\end{eqnarray}
where
\begin{eqnarray}
 z_n(\beta) = z_B (n \beta) +(-1)^{n+1} z_F (n\beta) .
 \end{eqnarray}
Here $z_B(\beta), z_F (\beta) $ are the single particle partition
functions of the bosonic and fermionic sectors respectively ( see \cite{Aharony:2003sx} for the explicit formulas for $z(\beta)$ in various gauge theories).

\par
If we introduce a chemical potential $\mu=(\log m)$, the formula for the partition function changes to
\begin{equation}
Z[\beta,\mu]=\int DU e^{(\sum_{n=1}^\infty {z_{n}(\beta,\mu) \over n} TrU^{n}TrU^{-n})}
\end{equation}
where
\begin{equation}
z_n(\beta,\mu)= z_B (n \beta,n \mu) +(-1)^{n+1} z_F (n\beta ,n \mu)
\end{equation}
$z_B(\beta,\mu), z_F (\beta,\mu) $ are now the single particle partition functions with chemical potential $\mu$. Hence
\begin{eqnarray}
z_B(\beta,\mu) &=& \sum_{bosons}{\rm exp}(-E_{i}\beta+Q_{i}\mu) \\
z_F(\beta,\mu) &=& \sum_{fermions}{\rm exp}(-E_{i}\beta+Q_{i}\mu)
\end{eqnarray}

$Q_{i}$ is the charge of the state whose energy is $E_{i}$ (see \cite{Aharony:2003sx}).

\par
As we have already mentioned, we wish to describe a system which has the same chemical potential $\mu$ for all three $U(1)$ charges of the R-symmetry group $SO(6)$ in grand canonical ensemble. Equivalently, we can work with fixed and equal values of the $U(1)$ charges in the canonical ensemble.
\par
Let us for simplicity confine ourselves to the bosonic sector of the $N=4$ SYM theory. The gauge fields have no R-charge. The six scalars $\phi_{i}$ $(i=1,...,6)$ can be grouped in pairs of two. We define
\begin{eqnarray}
\phi^{+}=\phi^{1}+i\phi^{2} ,
&&
\phi^{-}=\phi^{1}-i\phi^{2}
\end{eqnarray}
(We can similarly define complex fields for the other two pairs.) $\phi^{\pm}$ have charge $ \pm 1$ for each of the three commuting $U(1)s$ of $SO(6)$. Hence, if we consider the single particle partition function for these fields, it will be
\begin{equation}
z[x,\mu]=(exp(+\mu)+exp(-\mu)) z[x,0]/2
={\rm cosh}(\mu)z[x,0]
\label{chpt}
\end{equation}
where $z[x,0]$ is the single particle partition function without any chemical potential.

\subsection{Canonical Ensemble}
      We will now discuss the free gauge theory partition function for a  canonical ensemble with constant charge $Q_{0}$, by introducing a delta function $\delta(\widehat Q-Q_{0})$ in the functional integration of the gauge theory. $\widehat Q=Q[\phi]$ is the corresponding functional for the charge which we want to keep fixed. In our case $\widehat Q$ is just the functional for R-charge in gauge theory.
\par
The fixed charge partition function is defined by

\begin{eqnarray}
  Z(\beta,Q_{0}) &=& \int DX e^{\int_{0}^{\beta} S[X]} \delta(\widehat Q-Q_{0})  \\
 &=& \int DX e^{\int_{0}^{\beta} S[X]} \int {\rm exp}(i\mu \widehat Q){\rm exp}(-i\mu Q_{0})d\mu  \\
&=& \int d\mu {\rm exp}(-i\mu Q_{0})(\int DX e^{\int_{0}^{\beta} S[X]}e^{i\mu \widehat Q} ) \\
&=& \int d\mu {\rm exp}(-i\mu Q_{0})\int DU {\rm exp}(\Sigma z_{n}[\beta,i\mu]TrU^{n}TrU^{-n})
\label{chargefix1}
\end{eqnarray}
where $z_{n}[\beta,i\mu] = z^{V}_{n}[\beta,0]+cos(\mu)z^{S}_{n}[\beta,0]+\cos(\frac{\mu}{2})z^{F}_n[\beta,0]$.
\par
We can now make the approximation \footnote{This approximation can be thought of as a low temperature approximation. This is because at low temperatures $z^{S}_{n}[\beta,0]$ approaches zero as $e^{-\beta n}$. Hence the higher $z_{n}$ are suppressed relative to $z_{1}$. It is also true that for all temperatures,  $z_{n} < z_{1}$  and for very high temperatures we have $z_{n} \sim \frac{z_{1}}{n}$. As an example, the total contribution for all other $z_{n}$, even near hagedorn transition in free N=4 SYM  theory, is only about $7\%$ of $z_1$\cite{Aharony:2003sx}.
\par
Unitary matrix models involving $TrU^{n},n>1$ has been discussed in \cite{Jurkiewicz:1982iz,Mandal:1989ry}.
 } that $|z_{n}[x,i\mu]|$ for $n>1$ is negligible in comparison to $|z_{1}[x,i\mu]|$. Neglecting the contribution from the $n>1$ modes we arrive at a model which contains only $TrUTrU^{-1}$. Using the specific formula for $z[x,\mu]$, of the bosonic \footnote{Effect of the fermions is discussed in appendix \ref{app:fermion}.} sector ,
\begin{eqnarray}
\nonumber  Z(\beta,Q_{0}) &=& \int d\mu {\rm exp}(-i\mu Q_{0})\int DU {\rm exp}( (a+c\cos(\mu))TrUTrU^{-1}) \\
\nonumber &=& \int DU {\rm exp}(aTrUTrU^{-1})\int d\mu {\rm exp}(-i\mu Q_{0}){\rm exp}(c \cos(\mu)TrUTrU^{-1}) \\
&=& \int DU {\rm exp}(aTrUTrU^{-1})I_{Q_{0}}(c TrUTrU^{-1})
\label{IntegralZ}
\end{eqnarray}
Here $a(\beta)=z^{V}_{n}[\beta,0]$,$c(\beta)=z^{S}_{n}[\beta,0]$ and for convenience we did not show the explicit $\beta$ dependence in the equations. $I_n(x)$ is the Bessel function.
\par
Hence we end up with a matrix model with an effective potential
\begin{equation}
S_{eff}=a(TrUTrU^{-1})+\log[I_{Q_{0}}(c TrUTrU^{-1})]
\end{equation}
where $a>0,c>0$.
We define $\rho^{2}=TrUTrU^{-1}/N^{2}$ to get
\begin{equation}
S_{eff}(\rho)=N^{2}(a\rho^{2}+(1/N^{2})\log[I_{Q_{0}}(c N^{2}\rho^{2})])
\label{seff}
\end{equation}

It may seem that the logarithmic term is suppressed by a factor of $1/N^{2}$ and hence negligible for large N. But this need not be the case because, in the semicalssical large N limit, we must deal with a system with a charge of order $N^{2}$. Hence we define $Q_{0}=N^{2}q$ $(q \sim o(1))$. Using the asymptotic expansion of $I_{n}(nx)$ for large n, the effective action {\footnote{It should be noted that when Q=0 we should use the asymptotic expansion of $I_{0}(x)$ for large $x$. Then we get the expected answer $S_{eff}=(a+c)TrUTrU^{-1}$ which is same as a model without any constraint on charge.} becomes
\begin{equation}
S_{eff}(\rho)=N^{2}(a\rho^{2}+q(\sqrt{(1+\frac{c^{2}}{q^{2}}\rho^{4})}+\log(\frac{\frac{c}{q}\rho^2}{1+\sqrt{1+\frac{c^{2}}{q^{2}}\rho^{4}}})))+O(1)
\label{Seff}
\end{equation}
\subsection{Phase Structure}

To understand the phase diagram of this model at large N, we have to locate the saddle points of (\ref{Seff}) after including the relevant contribution from the path integral  measure depending on whether $\rho < \frac{1}{2}$ or $\rho > \frac{1}{2}$.\footnote{The term in the right hand side of equation (\ref{Tosolve2}) originates from the path integral measure over an unitary matrix.( see \cite{Goldschmidt:1979hq},Appendix of \cite{Alvarez-Gaume:2005fv}). }

Differentiating $S_{eff}(\rho)$  we get
\begin{eqnarray}
\nonumber \frac{\partial}{\partial\rho^{2}}S_{eff}(\rho)  &=& a+\frac{\partial}{\partial\rho^{2}}(\frac{1}{N^{2}}\log[I_{Q}(Q \frac{cN^{2}\rho^{2}}{Q})] \\
\nonumber  &=& a+b\frac{I_{Q}'(Q\frac{c\rho^{2}}{q}) } {I_{Q}(Q\frac{c\rho^{2}}{q})}  \\
 &=& a+\frac{q}{\rho^2}(1+\frac{c^{2}}{q^{2}}\rho^{4})^{\frac{1}{2}} +O(1/Q)
\label{Tosolve1}
\end{eqnarray}

\par
Hence the equations to solve are
\begin{eqnarray}
\nonumber a\rho+\frac{q}{\rho}(1+\frac{c^{2}}{q^{2}}\rho^{4})^{\frac{1}{2}} &=& \rho , \rho <\frac{1}{2} \\
a\rho+\frac{q}{\rho}(1+\frac{c^{2}}{q^{2}}\rho^{4})^{\frac{1}{2}} &=& \frac{1}{4(1-\rho)},\rho>\frac{1}{2}
\label{Tosolve2}
\end{eqnarray}

The left side in (\ref{Tosolve2}) can be written as

\begin{eqnarray}
a\rho+\frac{q}{\rho}(1+\frac{c^{2}}{q^{2}}\rho^{4})^{\frac{1}{2}}=
 a\rho+c\rho+\frac{q}{\rho}\frac{1}{(1+\frac{c^{2}}{q^{2}}\rho^{4})^{\frac{1}{2}}+\frac{c}{q}\rho^{2}}
\end{eqnarray}

So fixing the charge gives rise to a term of type
$\frac{q}{\rho}\frac{1}{(1+\frac{c^{2}}{q^{2}}\rho^{4})^{\frac{1}{2}}+\frac{c}{q}\rho^{2}}$ which has some important properties.
\begin{enumerate}
\item For all values of $q>0, c>0$, this term is a decreasing positive function of $\rho$ and it diverges as $\rho \rightarrow 0$.
\item For all values of $c>0$ it is a monotonically increasing function of $q$.
\end{enumerate}

We can now discuss the solution of this model at $N=\infty$. Let us assume that we are discussing the phase where $a(T)+c(T)<1$. This condition is valid for low temperatures since $a(T), c(T) \rightarrow 0$ as $T \rightarrow 0$. It should also be recalled that without any charge fixing the hagedorn transition occurs when $a(T)+c(T)=1$. Unlike the situation with no charge, here we have a function, on the left hand side of (\ref{Tosolve2}), which diverges as $\rho \rightarrow 0$. Hence $\rho = 0$ can not be a solution. We get only one solution at a finite value of $\rho$ which we will describe in the next paragraph.
\par
 Equation (\ref{Tosolve2}) is solved in the region $\rho<\frac{1}{2}$ with solution

\begin{eqnarray}
\rho^4=\frac{q^{2}}{(1-a)^{2}-c^{2}}=\frac{q^{2}}{(1-a-c)(1-a+c)}
\label{freesol}
\end{eqnarray}

The self consistency condition for a solution in the region $\rho < \frac{1}{2}$ is
\begin{eqnarray}
\rho^4=\frac{q^{2}}{(1-a)^{2}-c^{2}}<\frac{1}{16}
\label{Selfconst}
\end{eqnarray}

 At low temperatures the condition is naturally satisfied for a small enough value of $q$. If we gradually increase the temperature (i.e. the value of $a(T)$ and $c(T)$) while keeping the value of the $q$ fixed, then the value of $\rho$ at this saddle point will increase. At some temperature $T_3(q)$, $\rho$ will become equal to $\frac{1}{2}$. Since the measure part (i.e. right hand side of (\ref{Tosolve2}) ) has a third order discontinuity at $\rho=\frac{1}{2}$, we will get a third order phase transition at the temperature $T_{3}$. From (\ref{Selfconst}) we have the following condition at $T_{3}$
\begin{eqnarray}
\frac{q^{2}}{(1-a)^{2}-c^{2}}=\frac{1}{16}
\end{eqnarray}
 If the temperature is increased beyond $T_{3}$ then we have to solve (\ref{Tosolve2}) in the region $\rho > \frac{1}{2}$.
\par
If we increase $q$, then the value of $\rho$ at the saddle point for a fixed temperature will increase. At some $q_{3}$ we get a third order phase transition satisfying
\begin{eqnarray}
16q_{3}(T)^2=(a-1)^2-c^2
\end{eqnarray}
Since the minimum value of $a(T)$ and $c(T)$ is zero, the maximum possible value of  $q_{3}^{2}(T)$ is $q_{crit}^{2}=\frac{1}{16}$. If we increase the $q$ beyond $q_{crit}$, the saddle point will always be confined in the parameter range $\rho > \frac{1}{2}$. Consequently as we increase the temperature from zero we will not get a third  order phase transition for  $q > q_{crit} = \frac{1}{4}$.

\par
This free model, at zero gauge coupling ($l_{s}>>R$ in bulk), has some similarities with $AdS_{5}$ black holes in a fixed charge ensemble. However  unlike the three black hole branches in $AdS_{5}$, we get only one branch in the free theory. But most importantly the solution always has a nonzero value of $\rho$.

It should be recalled that before the Hagedorn transition, a free gauge theory with zero charge has the solution $\rho=0$ \cite{Sundborg:1999ue,Aharony:2003sx}.
\par
Some properties of the free theory will be important when we analyze the situation for the weakly coupled gauge theory. Just above the temperature $T_{3}(q)$,  the difference of the two sides of (\ref{Tosolve2}) can be expanded in the region $\rho > \frac{1}{2}$. Defining $\rho=\frac{1}{2}+x$,($x>0$) the difference is
\begin{eqnarray}
-\epsilon(q)x-C_{1}x^{2}
\label{expansion}
\end{eqnarray}
Here $\epsilon(q)>0$ and $\epsilon(q)  \rightarrow 0$ as $q \rightarrow 0$. It is important to note that $C_{1}> 2$ because the measure function (i.e. right hand side of (\ref{Tosolve2}) has a third order discontinuity at the point $\rho=\frac{1}{2}$. We will also discuss the significance of this in what follows.

\section{Small coupling model}\label{sec:small}

We will now discuss the problem with a small non-zero gauge coupling $\lambda=g_{YM}^{2}N$. By AdS/CFT correspondence it corresponds to a finite string length in $AdS$. It has been shown in \cite{Alvarez-Gaume:2005fv} that by considering a phenomenological model of type
\begin{eqnarray}
S[TrUTrU^{-1}] = a(\lambda,T)(TrUTrU^{-1})+\frac{b(\lambda,T)}{N^2}(TrUTrU^{-1})^2 , b>0
\label{liuwa}
\end{eqnarray}
we can map out the possible phase diagram of type $IIB$ string theory in $AdS_{5}$.\footnote{In fact in \cite{Alvarez-Gaume:2005fv} an arbitrary convex function is considered, and shown to map out the phase diagram of $IIB$ theory in $AdS_5$. The simplified model (\ref{liuwa}) leads to similar qualitative result.} Even though the model in (\ref{liuwa}) can be derived from a weak coupling analysis of the gauge theory, it can be thought of as a phenomenological model describing supergravity in $AdS_{5}$.
\par
 We are motivated to discuss the fixed charge ensemble in the same spirit. Let us add a small interaction term to (\ref{seff}). The effective action is then given by
\begin{eqnarray}
S_{eff}(\rho)=N^{2}(a\rho^{2}+b\rho^{4}+q(\sqrt{(1+\frac{c^{2}}{q^{2}}\rho^{4})}+\log(\frac{\frac{c}{q}\rho^2}{1+\sqrt{1+\frac{c^{2}}{q^{2}}\rho^{4}}})))+O(1)
\label{SeffInt}
\end{eqnarray}
Here $b$ is proportional to $\lambda$ and is also a function of charge. Depending on the theory considered, the sign of $b$ can be either positive or negative. It has been shown in \cite{Aharony:2005bq} that $b$ is positive for a pure YM theory. In the following discussion we will assume that this is the case in order to motivate a similarity with the supergravity picture.
The equations determining the saddle points of (\ref{SeffInt}) , including the contribution from the path integral measure, are

\begin{eqnarray}
\nonumber (a+c)\rho^2+2b\rho^4+\frac{q}{(1+\frac{c^2}{q^2}\rho^{4})^{\frac{1}{2}}+\frac{c}{q}\rho^{2}}  & = &  \rho^2, \rho <\frac{1}{2} \\
    (a+c)\rho^{2}+2b\rho^{4}+\frac{q}{(1+\frac{c^2}{q^2}\rho^{4})^{\frac{1}{2}}+\frac{c}{q}\rho^{2}} & = & \frac{\rho}{4(1-\rho)}, \rho > \frac{1}{2}
\label{TosolveInt}
\end{eqnarray}
\par
In what follows it will be useful to introduce a function
\begin{eqnarray}
\nonumber M(\rho) & = & \rho^{2}, \rho <\frac{1}{2} \\
        & = & \frac{\rho}{4(1-\rho)},\rho>\frac{1}{2}
\end{eqnarray}
$M(\rho)$ is an increasing convex function and is the right hand side of (\ref{TosolveInt}). It is also useful to introduce $D(x)=S'_{eff}(x)-M(x)$. Eqn (\ref{TosolveInt}) is then equivalent to $D(\rho)=0$.
\par
It has been shown in \cite{Alvarez-Gaume:2005fv} that for an interacting model with zero charge, we get nucleation of black holes along the curve given by $a=\frac{1-2w}{(1-w)^{2}(1+w)}$ and $b=\frac{2w}{(1-w)^{2}(1+w)^{3}}$, $1>w>0$. Here we want to analyze a similar type of phenomenon. Let us consider the different cases.
\par

\subsection*{\underline{$T$ is varying and $q$ is small}}
\par

Let us start with a value of charge which is small (i.e. $q \ll 1$) and let us increase the temperature from zero. At low temperatures all the parameters $a, c$ will be small (for small $T$ these parameters have a dependence like $e^{-c\beta}$, $c$ is a constant ). Hence we get just one solution for $\rho < \frac{1}{2}$ which we call $I$. There is no solution for $\rho > \frac{1}{2}$ (see the topmost curve of Fig \ref{Fixedq}) because the left hand side of (\ref{TosolveInt}) is less than the right hand side.
\par
The situation is quite similar to supergravity where for small charge and low enough temperatures we get a stable small black hole solution. \footnote{We should keep in mind that $\rho < \frac{1}{2}$ is not the supergravity regime. The solutions of gauge theory effective action there should be represented as excited string states.}

\begin{figure}[h!]
\begin{center}
\includegraphics[height=2in]{Solution_fixedq.ps}
\end{center}
\caption{Plots of $D(\rho)$ with increasing $a=c$ from the above and with fixed $b$ and $q<q_{crit}$}
\label{Fixedq}
\end{figure}

The function $M(\rho$) (i.e. right hand side of (\ref{TosolveInt})) is a convex increasing function. Hence we will generate new solutions of (\ref{TosolveInt}) in the region $\rho > \frac{1}{2}$ as we increase temperature (i.e. $a(T),c(T)$ as discussed in appendix \ref{app:genprop}) keeping $q$ fixed (\fig{Fixedq}, \fig{Fixedq1}). The new solutions will always come in pairs (Fig \ref{Fixedq}). Let us call the solution nucleation temperature as $T_{01}(q)$. At $T=T_{01}$ we have
\begin{eqnarray}
\nonumber D(\rho)=S_{eff}'(\rho)-M(\rho) &=& 0 \\
    D'(\rho)=0
\end{eqnarray}

\begin{figure}[h!]
\begin{center}
\includegraphics[height=2in]{Solution_fixedq1.ps}
\end{center}
\caption{ Top three graphs of Fig $2$ showing emergence of two saddle points in the region $\rho > \frac{1}{2}$ }
\label{Fixedq1}
\end{figure}
\par
As we increase the temperature further (i.e. $a(T), c(T)$) the function on the left hand side of (\ref{TosolveInt}) will also increase. Hence the solutions will start to separate. Let us call them $II$ and $III$. Here $\rho_{III}>\rho_{II}$. Also, $III$ is a stable saddle point whereas $II$ is an unstable one. They are similar to stable big and unstable small black holes in supergravity. As the temperature is increased beyond $T_{01}$ the value $\rho_{II}$ decreases whereas $\rho_{III}$ increases. At some temperature $T_{H}(q)$, we will have $S(III)<S(I)$ and consequently we expect a first order phase transition.  At a temperature $T_{HP}$, the dominant saddle point of the system changes from $I$ to $III$. As the temperature increases the saddle point $II$ goes through a third order transition when $\rho(II)$ crosses the $\rho={1 \over 2}$ point. Call this temperature $T_{3}$ which is determined by the following relation between the parameters

\begin{eqnarray}
(a+\frac{b}{2})+4q(1+\frac{c^{2}}{16q^{2}})^{\frac{1}{2}}=1
\end{eqnarray}
\par
Increasing the temperature further, the saddle point $II$ approaches the saddle point $I$ and they merge  at a temperature $T_{02}$ ($4th$ graph from above in Fig \ref{Fixedq} ). In the language of catastrophe theory this is a fold
 catastrophe. For $T>T_{02}$, the only saddle point is $III$. This then is the thermal history as we increase the temperature for a small $q$.
\par
In summary at low temperatures, we have only one saddle point $I$ and then two new saddle point $II,III$ are created at $T_{01}$. As the temperature increases the saddle points $I , II$ merge at a temperature $T_{02}$. Beyond that we have only one saddle point $III$. In the next paragraph we will discuss what happens when we increase the value of the $q$.

\subsection*{\underline{Varying q$:$}}
\par
     Let us discuss how the various temperatures discussed above change as we increase the value of $q$.
\begin{enumerate}

\item The first is $T_{01}(q)$, the nucleation temperature for saddle points $II$ and $III$. $T_{01}$ will decrease as we increase the value of $q$. This is so because all three terms in the right hand side of (\ref{TosolveInt}) are positive and increasing functions of $\rho$ and the left hand side is a positive convex function. Consequently the saddle point value of $\rho$ at $T_{01}$ will also decrease.

\item The temperature $T_{02}$ at which the stable saddle point $I$ and unstable saddle point $II$ merge and the value of $\rho$ at $T_{02}$, will increase as we increase $q$. The reason is that all the coefficients in (\ref{TosolveInt}) are positive and hence increasing the value of $q$ increases the function on the left hand side.

\end{enumerate}

\par
 As we increase the value of $q$ further, $T_{01}$ and $T_{02}$ will become equal for some value of $q=q_{crit}$. In the language of catastrophe theory this is a cusp catastrophe. Corresponding to $q_{crit}$ there will be a $T_{crit}=T_{01}=T_{02}$ and a value of $\rho_{crit}$ (saddle point $\rho$ at $q_{crit}$ , $T_{crit}$).  As we increase the $q$ beyond $q_{crit}$, we do not get any new saddle point and consequently  there is only one saddle point for all temperatures. We will discuss the physics near this phase transition in detail in what follows.
\par

\subsection*{\underline{Value of $\rho_{crit}$ :}}

Let us determine the value of $\rho_{crit}$. As already discussed at the end of the previous chapter, in (\ref{expansion}) $C$ is always a finite quantity. Hence, (\ref{TosolveInt}) cannot have three solutions in the region $\rho<\frac{1}{2}$ for small $b$. Therefore the saddle point $I$ is always in the region $\rho < \frac{1}{2}$. Whereas the saddle point $III$ will be in the region $\rho>\frac{1}{2}$. Hence the only place where these three saddle points can meet is $\rho_{crit}=\frac{1}{2}$ which is also the point of the third order phase transition.

\vspace{0.5cm}
\subsection*{\underline{Physical Interpretation}}
\par
Before proceeding further we will briefly discuss the bulk interpretation of saddle points of weakly coupled gauge theory. Weak coupling in gauge theory means $l_{s}\gg R_{AdS_{5}}$. Hence the supergravity picture is not valid in the bulk. However at large $N$, the string coupling (i.e. $\frac{1}{N}$) will be small and we may conclude that the saddle points discussed above can be described by exact (in all orders in $l_{s}$) conformal field theories. These CFTs  are characterized by the values of  $q$ and $\rho$ at the saddle points.

\par

We would like to end this section by emphasizing that the coincidence of the three saddle points at $\rho=\frac{1}{2}$, is a property of the weak coupling ($\lambda << 1$) limit of the gauge theory. In what follows we will see that this fact is not necessarily true at strong coupling. We will show that there the coincidence happens in the gaped phase where $\rho>\frac{1}{2}$.

\section{Effective action and phase diagram at strong coupling} \label{sec:simmod}

In this section we will discuss the effective action and the phase diagram in the strongly coupled gauge theory which is dual to the supergravity (discussed in section \ref{Supergravity}) regime of $IIB$ string theory.
\subsection{ Finite temperature effective actions in the gauge theory}
\par
Let us first summarize the situation in the zero charge sector. The propagator of adjoint fields in the free gauge theory, on a compact manifold $S^{3}$, coupled to a space independent $A_{0}$ is given by (see \cite{Kazakov:2000pm})
\begin{eqnarray}
G^{ij}_{U ~ kl}(x,t,y,0)=\sum_{n=-\infty}^{n=\infty} (U^{n})^{i}_{j} G_{0}(x,t+n\beta,y,0) (U^{-n})^{k}_{j}
\label{green}
\end{eqnarray}
 where $G_{0}(x,t,y,0)$ is the zero temperature Green's function and $U$ is the constant Polykov line. We know that at any temperature \footnote{Temperature here is measured in units of $\frac{1}{R_{S^{3}}}$.} $G_{0}(x,t+n\beta,y,0) > G_{0}(x,t,y,0) $ and also at low temperatures
\begin{eqnarray}
G_{0}(y,t+n\beta,x,0) \sim e^{-n\beta}
\label{lowtemp}
\end{eqnarray}
Using the above Green's function one can develop the large N diagrammatic to arrive at an effective action involving $Z_N$ invariant terms built out of products of $trU^n$. In fact one can imagine integrating out all the modes $trU^n$ for $n>1$ in favor of $trUtrU^{-1}$. In this way one gets an effective action of the form
\begin{eqnarray}
S_{eff}=\sum_{n=1}^{n=\infty} a_n(\beta,\lambda) (\frac{TrUTrU}{N^2})^n
\end{eqnarray}

As one increases the coupling constant we would expect that the form of the effective action would remain the same except that the dependence of the parameters on temperature and the 'thooft coupling would change.
\subsection{Non-zero charge sector}
\par
If we include the fixed charge constraint, as in (\ref{chargefix1}), then we get the following expression for the fixed charge path integral
\begin{eqnarray}
Z_{q}=\int d\mu e^{i\mu Q}\int DU e^{N^{2}(\sum_{n=0}^{n=\infty} S_{n}(\rho,\lambda,\beta) \cos(n\mu))}
\label{stract}
\end{eqnarray}
For large $N$ we can do the $\mu$ integral by the saddle point method. The saddle point of $\mu$ is on the imaginary axis. Hence we set $\mu=im$, to get the saddle point equation
\begin{eqnarray}
q=\sum_{n=1}^{n=\infty} nS_{n}(\rho,\lambda,\beta) {\rm sinh} (nm)), q=Q/N^{2}
\label{GenSaddle}
\end{eqnarray}
At small values of $\rho$, $S_{n}(\rho)$ goes as $\rho^{n}$ \footnote{Introduction of a chemical potential changes the formula (\ref{green}) as
\begin{equation}
\nonumber G^{\mu ~ ij}_{U ~ kl}(x,t,y,0)=e^{\frac{i\mu t}{\beta}} \sum_{n=-\infty}^{n=\infty} (U^{n})^{i}_{j} G^{\mu}_{0}(x,t+n\beta,y,0) (U^{-n})^{k}_{j}
\end{equation}
 where
\begin{equation}
G^{\mu}_{0}(x,t+n\beta,y,0)=e^{i n \mu}G_{0}(x,t+n\beta,y,0)
\end{equation}
Hence in each order in perturbation theory the terms containing $\cos(n \mu)$ also get multiplied by
$(TrUTrU^{-1})^{m},m>n$ or the higher operators like $TrU^{n}$ which can be integrated out to give again a term like $(TrUTrU^{-1})^{m}$.
  } and hence in the $\rho \rightarrow 0$  limit  we can approximate the equation (\ref{GenSaddle}) as
\begin{eqnarray}
q \approx {\cal C} \rho {\rm sinh} (m)
\end{eqnarray}
where ${\cal C}$ is a constant independent of $\rho$.
The solution is
\begin{eqnarray}
m \approx q\log(\rho)+{\cal C} , \rho \rightarrow 0
\end{eqnarray}
Substituting $m$ in ($\ref{stract}$) we get a logarithmic term for $\rho$. We conclude that the logarithmic term is a general feature and it implies among other things that $TrU=0$ is never a solution in the non-zero charge sector.

\subsection{Model effective action at strong coupling}
\par
Following our previous discussion, we will include the generic logarithmic term in the effective potential for a fixed non-zero charge, and proceed to analyze the saddle point structure following \cite{Alvarez-Gaume:2005fv}.

Our proposal for the gauge theory effective action is
\begin{eqnarray}
S_{q}=S(a(T),b(T),...,\rho)+q\log(\rho)
\end{eqnarray}
and the saddle point equations are
\begin{eqnarray}
\nonumber \rho F(a(T),b(T),c(T),...\rho^2)+q  =\rho^{2} , \rho <\frac{1}{2} \\
\rho F(a(T),b(T),c(T),...\rho^2)+q =\frac{\rho}{4(1-\rho)},\rho>\frac{1}{2}
\label{TosolveIntStr}
\end{eqnarray}
Where $F(\rho)=S'_{eff}(\rho)$. We assume that
\begin{enumerate}
\item{ $F(x,T)$ is a monotonically increasing function of $x$ and F(0,T)=0}
\item{ Value of $F(x,T)$ increases for fixed $x$ as we increase the temperature and F(x,0)=0.}

These global properties of $F(x)$ reproduce the phase diagram of supergravity.

\end{enumerate}
\par
\subsection*{\underline{Analysis of solution structure}}

\par
     Let us consider the function $D(T,\rho)=\rho F(\rho,T)-M(\rho)$ (Where $M(\rho)$ is the contribution from measure appearing at the right hand side of (\ref{TosolveIntStr})). At $T=0$, $F(\rho,T)$ is zero. Hence  $D(T,\rho)$ is a monotonically decreasing function of $\rho$ at $T=0$.
\par
 We know that at $T=T_{01}$ a pair of  two new saddle points appear at $\rho_{01}>\frac{1}{2}$. Hence at $T=T_{01}$ we have $D(T_{01},\rho_{01})=0$ and $D'(T_{01},\rho_{01})=0$. $D(T_{01},\rho)$ has a zero for $\rho=0$   and it is a decreasing function in the neighborhood of $\rho=0$. It again increases and become zero at $\rho_{01}$ and then the function again decreases as $\rho \rightarrow 1$. This implies that the function has a local maximum and local minimum.

\begin{figure}[h!]
\begin{center}
\includegraphics[height=2in]{emergence.ps}
\end{center}
\label{Emergence}
\caption{Plots of $D(T,\rho)$ for $T=0$, $T=T_{crit}$,$T=T_{01}$ from below.}
\end{figure}

\par
In summary:
\begin{enumerate}
\item{$D(0,\rho)$ is a monotonically decreasing function of $\rho$.}
\item{$D(T_{01},\rho)$ has a maximum and minimum.}
\end{enumerate}
\par
There is a temperature $T_{crit}$ at which the local maximum and local minimum appear (Fig \ref{Emergence}). Let us call this temperature $T_{crit}$. At $T_{crit}$ the curve $D(T_{crit},\rho)$ will have a point of inflection at $\rho=\rho_{crit}$, say. Let the value of $D(T_{crit},\rho_{crit})=q_{crit}$.
\par
Increasing the  value of $q$ from zero we need to solve the equation $D(T,\rho)=q$. We will get a solution for a non-zero value of $\rho$. Denote this solution as $I$. As the temperature increases, two new solutions  appear at $T=T_{01}$. Call the stable solution as $III$, and the unstable solution $II$. As  the temperature is further increased to $T_{02}$, the unstable solution $II$ and the stable solution  $I$ merge.  For $T>T_{02}$ , the only solution is $III$.
 \par
 As $q$ approaches $q_{crit}$ from below the two temperatures $T_{01}$ and $T_{02}$ approach each other.  At $q=q_{crit}$, we have $T_{01}=T_{02}=T_{crit}$. If we increase $q$ beyond $q_{crit}$ only one solution appears for all temperature. These facts are consistent with supergravity solutions(section \ref{Supergravity}).
\par
 With a sufficiently sharp rising function $F(T,\rho)$ in (\ref{TosolveIntStr}) we can obtain this critical point in the region $\rho>\frac{1}{2}$.\footnote{Which describes supergravity in the bulk\cite{Alvarez-Gaume:2005fv}.}. As the function $D(\rho,T)$ is smooth in the region $\rho>\frac{1}{2}$ the second derivative of the function $D(T,\rho)$ will vanish at the inflection point, and we will get a third order phase transition. We can calculate the partition function in suitable double scaling limit near the critical point. This is discussed in section \ref{Unin}.
\par
\subsection*{\underline{A specific example}}

We will now illustrate the above phenomenon in a simple model defined by
\begin{eqnarray}
F(\rho)=a\rho+b\rho^{3}
\label{newmod}
\end{eqnarray}
where $a,b > 0$.

We will determine the parameter ranges of $a,b$ for which all the three saddle points of (\ref{newmod}) are in the range $\rho>\frac{1}{2}$.

\begin{figure}[h!]
\begin{center}
\includegraphics[height=2in]{Tricritical_fixedT.ps}
\end{center}
\label{Tricritical}
\caption{Plots of $D(T,\rho)$ with with fixed $a$ and increasing $b$ from the top, showing a critical transition in the region $\rho>\frac{1}{2}$ (from the top, the $3rd$ graph has a point of inflection) }
\end{figure}

At $\rho=\frac{1}{2}$ we have the constraints

\begin{eqnarray}
\nonumber \partial_{\rho}(\rho F(\rho)-\frac{\rho}{4(1-\rho)})<0 \\
\partial_{\rho}^{2}(\rho F(\rho)-\frac{\rho}{4(1-\rho)}>0
\label{rho}
\end{eqnarray}
Putting the value of $\rho=\frac{1}{2}$ in the above inequality we get the following constraints on the parameters $a+b<1$ and $a+3b>2$. Simplifying we have $b>\frac{1}{2}$ and $a<\frac{1}{2}$.

 \par
As the coupling become stronger, we expect that $b$ is not necessarily small and will be of $o(1)$ or greater. All the saddle points of (\ref{TosolveIntStr}) are then naturally shifted to the region $\rho>\frac{1}{2}$. Here, as was discussed in \cite{Alvarez-Gaume:2005fv}, we can expect to match the solutions of the gauge theory with those of supergravity. The stable saddle point $I$ corresponds to the stable black hole branch $I$ of supergravity. And unstable saddle point $II$ is matched with the unstable black hole branch $II$. The stable saddle point $III$ is matched with the big stable black hole in supergravity. With this identification the thermal history and critical behavior of the gauge theory, discussed earlier in this chapter, match with the thermal history and critical behavior of supergravity (discussed in section \ref{Supergravity} and \cite{Chamblin:1999hg}).

\section{Universal neighborhood of critical point and the critical exponents}\label{Unin}

Let us consider the effective action $S_{tot}(\rho,T,q)$ which includes the contribution from the path integral measure over an unitary matrix. The derivative of $S_{tot}$ with respect to $\rho$, say $G(\rho,T,q)$, gives the saddle point equations (\ref{TosolveIntStr}). We have already discussed that by a suitable choice of parameters the critical point appears in the region $\rho>\frac{1}{2}$. This critical point is a third order critical point because three saddle points of the system merges here. Hence the first and second derivatives of $G_{tot}(\rho,T,q)$ with respect to $\rho$ vanish at $\rho=\rho_{crit}, q=q_{crit},T=T_{crit}$. Expanding $G(\rho,T,q)$ around the critical point , we get
\begin{equation}
G(\rho,T,q)=(\delta \rho)^{3}\frac{\partial^{3}_{\rho}G}{3!}+(\delta T)\partial_{T}G+(\delta q)\partial_{q}G+(\delta\rho)(\delta T)\partial_{\rho}\partial_{T}G+(\delta q)(\delta T) \partial_{\rho}\partial_{q}G
\label{Geq}
\end{equation}

 \par
Let us fix $T=T_{crit}$ or $\delta T=0$. Then the equation (\ref{Geq}) has one solution. In order to know how the saddle point value of $\rho$ approaches $\rho_{crit}$ ($\delta \rho \rightarrow 0$) as $\delta q \rightarrow 0$, we equate the leading part of (\ref{Geq}) to zero.
\begin{eqnarray}
(\delta \rho)^{3}\frac{\partial^{3}_{\rho}G}{3!}+(\delta q)\partial_{q}G=0
\end{eqnarray}
Hence $\delta \rho \propto \delta q^{\frac{1}{3}}$ and we get the same universal exponent $\frac{1}{3}$ as in supergravity \cite{Chamblin:1999hg}.

\subsection{Partition function near the critical point}
Near the critical point we can write the $S_{tot}$ as
\begin{eqnarray}
S_{tot}=S_{tot}(\rho_{crit},T_{crit},q_{crit})+(\delta\rho)^{4}\frac{\partial^{4}_{\rho}S}{4!}+(\delta q )\partial_{q}S+(\delta q)(\delta \rho)\partial_{\rho}\partial_{q}S+O(\delta \rho^5)
\label{Seq}
\end{eqnarray}
If we define a double scaling limit $N^\frac{1}{2}\rho=x,N^{\frac{3}{2}}q=z$ , we can write the $o(1)$ part of the partition function, after suitable rescaling of the variables, as
\begin{eqnarray}
Z_{2} \propto && \int dx e^{-(x^4-zx)}
\end{eqnarray}
This can be calculated in a power series
\begin{eqnarray}
Z_{2} \propto \sum_{n=0}^{\infty} \frac{z^{2n}}{(2n)!} \Gamma (\frac{n}{2}+\frac{1}{4})
\end{eqnarray}

\subsection{Approaching the critical point through a line of first order transitions}
\par
Another type of double scaling limit is possible in this problem. We can set\footnote{It is same as following the HP(first order) transition line in parameter space.}
\begin{eqnarray}
(\delta T)\partial_{T}G+(\delta q)\partial_{q}G=0
\label{rel}
\end{eqnarray}
by choosing a suitable relation between $\delta T$ and $\delta q$. Using (\ref{rel}) in (\ref{Geq}) we get
\begin{eqnarray}
 (\delta \rho)^{3}\frac{\partial^{3}_{\rho}G}{3!}+(\delta\rho)((\delta T)\partial_{\rho}\partial_{T}G+(\delta q)\partial_{\rho}\partial_{q}G)=0
\end{eqnarray}

with the solutions
\begin{eqnarray}
\nonumber \delta \rho=0 \\
\delta \rho \propto \pm(\delta T)^{\frac{1}{2}}
\label{prop}
\end{eqnarray}

We can expand $S_{eff}$ as
\begin{eqnarray}
S_{eff} \approx S_{crit}+(\delta\rho)^{4}\frac{\partial^{4}_{\rho}S}{4!}+C_{1}(\delta T)(\delta \rho)^{2}+ OT
\end{eqnarray}
where $OT$ are terms independent of $\delta\rho$. Defining a suitable double scaling limit. $N^{\frac{3}{2}}\delta T=z, N^{\frac{1}{2}}\delta\rho=x$ and a suitable rescaling of the parameters we can evaluate the $o(1)$ factors in the partition function as
\begin{eqnarray}
Z_{2} \propto \int dx e^{-(x^{4}+2 z x^2)} \propto \sum_{n=0}^{\infty} \frac{(2z)^{n}}{n!} \Gamma (\frac{n}{2}+\frac{1}{4})
\propto \sqrt{z}e^{\frac{z^{2}}{2}}K_{\frac{1}{4}}(\frac{z^{2}}{2})
\end{eqnarray}

where $z<0$.

\section{Conclusion}
\par
In this paper we have studied the logarithmic matrix model generated by fixing the R-charge in the gauge theory partition function. In the free gauge theory it has been shown that there is no solution with $\rho=0$ ($AdS$ type solution). We then studied the effect of adding an interaction term in our model and discussed the generic nature of the logarithmic term even at arbitrary value of the coupling. We identified the supergravity saddle points and their critical behavior which was discussed in (\cite{Chamblin:1999hg}).
\par
  Our main aim was to give another example of the utility of unitary matrix methods in providing a non-perturbative dual description of blakholes in $AdS$ and to understand the relation between matrix models and string theory in general. It would be interesting to consider an effective unitary matrix model to describe phases of Kerr-Ads black holes.

\section{Acknowledgment}
 We would like to thank the theory division of CERN for hospitality where part of this work was done. We acknowledge useful discussions with Luis Alvarez-Gaume and Marcos Marino on many aspects of the matrix model/string theory correspondence. We also acknowledge a correspondence with Hong Liu. PB likes to acknowledge CSIR for SPM fellowship and TIFR alumni association for partial financial support. PB also likes to thank Swagato Mukherjee for technical help in preparation of this paper.

redpajama_set_name: RedPajamaArXiv


text:
Furniture Fail: UK Store Uses Iran to Sell Things You Can't Afford
By Caroline Stanley
While we're sure this has been happening across the board, the BBC reports that Habitat (the European furnishings franchise founded by Terence Conran in the '60s, now part of the IKANO Group) added fake hashtags to tweets — like "Iran" and "Tehran" — so that more people would see information about their spring collection sales.
An example tweet: "HabitatUK: #MOUSAVI Join the database for free to win a £1,000 gift card."
The retailer is playing dumb; per their official statement: "This was absolutely not authorised by Habitat – we were shocked when we discovered what happened."
PS: If you haven't yet, show your support for the people who fight for democracy in Iran via a greened Twitter icon.

redpajama_set_name: RedPajamaCommonCrawl


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Your overdenture is a removable denture, and can fit over a small number of remaining natural teeth or implants. If using your natural teeth, these may be prepared to provide stability and support for the overdenture.
With all forms of denture assessment, your dental prosethetis will conduct a thorough examination of your jaw line, teeth structure and mouth wellbeing. This helps us to provide you with the best possible denture solutions and suggest options to support your overdenture.
What are the Benefits to Using Implant Overdentures?
Improved digestion – if your dentures are held by using adhesives, you might be interested to know that overdentures use dental implants, making them more stable than adhesive held dentures. This allows you to chew food thoroughly, assisting the breakdown of food in your stomach and absorb more nutrients.
Reduced bone loss – your overdenture simulates and stimulates your jaw bone when you chew. This reduces and stops shrinkage which is generally the result of missing teeth.
Retained facial structure and features – missing teeth can cause your face to appear 'sunken' and prematurely aged as the area between your nose and chin shrink.
Call us for an appointment to discuss dental implants and an overdenture.


Kolkata, 27th March, 2018: Vakrangee Limited through its wholly owned subsidiary company "Vakrangee Logistics Private Limited" ("VLPL") has entered an alliance with Blue Dart Express Limited to offer last mile courier and logistics services on a PAN India basis.
As per the arrangement with Blue Dart, VLPL through Vakrangee Kendras will offer courier pick-up and delivery services to the citizens – more affordably, reliably & efficiently. In the first phase, VLPL in collaboration with Blue Dart plans to roll out last mile delivery services across selected locations in Maharashtra, which will further be extended to cover the entire network of Vakrangee Kendras across the country. This association will allow Blue Dart to extend their reach to un-served and under-served areas through Vakrangee Kendras. Parallelly, this alliance will benefit Vakrangee Limited by further expanding their bouquet of services for citizens.
Vakrangee is a technology driven company, focusing on creating India's largest network of last mile retail points-of-sale. The company's aim is to potentially enable every Indian to seamlessly benefit from financial inclusion, social inclusion, digital India, skill development, employment, government programs and a wider access to basic goods and services. It is the third largest franchisee network globally with more than 44000 Vakrangee Kendras in more than 17 states. The company endeavours to bridge the financial inclusion gap between the developed urban India and the under-developed rural India through Vakrangee Kendras.
Blue Dart Express Limited, South Asia's premier courier, is an integrated express package distribution company. Its extensive domestic network covers over 35000 locations, and services in more than 220 countries and territories worldwide through their group company DHL, the premier global brand name in express distribution services.


Defence Turkey: How important is the defence and security relationship with Turkey?
Turkey and the United Kingdom enjoy well established relations based on the NATO alliance, strategic partnership, mutual economic interests and shared security concerns. The future presents ample opportunities for further enhancement of the bilateral relations. Defence and security, large infrastructure projects like airports, health, nuclear energy and finance sectors will be at the forefront of the economic co-operation between the two countries. It is essential that we work together to help support global challenges and also the important interoperability needs of both armed forces.
Defence Turkey: In the defence and security sector what is the most prominent example of the countries and companies working together?
Last year Turkish Aerospace Industries and BAE Systems signed a contract for the design of the TF-X programme which Turkey has stated will be an important part of their modernisation programme. Discussion is now ongoing on the appropriate engine. The recent visit by the Turkish President highlighted the importance of this programme and the need for further industrial co-operation between the United Kingdom and Turkish companies both in this programme but also in other areas where these partnerships can satisfy the future aspirations of the Turkish armed forces.
The sharing of information is also an important dimension of the strategic defence relationship between the United Kingdom and Turkey, as underlined by the 2016 General Security Agreement.
Defence Turkey: Both countries are modernizing their armed forces, what can you say about your procurement plans and is there information sharing to learn from each other's procurement practices?
The global defence industry is one of the most lucrative in the world, with expenditure exceeding $1.57 trillion in 2016.The defence procurement market in the UK alone is worth around £20 billion; in fact the United Kingdom Ministry of Defence (MOD) is UK industry's single largest customer. The United Kingdom Ministry of Defence is also committed to spending around £178bn over the next 10 years as part of their Equipment spending plan to deliver large scale Defence procurement projects and unlock the MOD supply chain for small and medium sized companies. The United Kingdom is happy to share its experiences over the last years in ensuring that it has got value for money, supports companies both large and small and encourages innovation to help current and future programmes. Turkey may have the same aspirations so learning from each other is very beneficial. The United Kingdom also encourages foreign companies to consider supplying to their armed forces and there are no barriers for Turkish companies and I would strongly encourage them to respond to the link www.contracts.mod.uk where they can register to receive the Defence Contracts Bulletin which outlines opportunities.
Defence Turkey: Is there regular engagement of both armed forces?


How can libraries and archives prepare for emerging scholarly fields that haven't yet emerged? How do we know when such a "discipline" is emerging, and how might we support it?
An archivist at Special Collections and the history/social science librarian at the Virginia Tech Libraries saw signs of research interest about veterans on their campus and elsewhere. With an interest in supporting what might be considered an emerging field, both were aware of the risks of investing in materials that do not attract users. This presentation will examine their process of evaluating those risks while assessing evidence of a growing need. After a review of existing holdings, they began to survey the research landscape for indications of the subjects, disciplines, methods, and constituencies that might consolidate as a discrete field of veterans studies. Further, given the absence of indicators that mark established fields—regular conferences, journals, academic programs—they turned towards a strategy of actively "seeding the need" by engaging in interdisciplinary conversations on the matter of veterans studies and gauging reaction and participation. As a consequence of this work, both librarian and archivist have become active in projects that are creating the very indicators that suggest veterans studies may emerge as a field of academic inquiry requiring library support. At this session, this process and its results to date will be discussed, along with the project's implications for special and circulating collections and, more broadly, the library's scholarly communications initiatives.


Whether you're creating scrapbooks or cards, you need beautiful specialty paper to make your projects stand out. Discover all the designs and colors you can find for your paper craft projects when you shop at HSN. To create depth and layers in your scrapbooks, pick up some card stock for thickness and add specialty paper on top for a unique design. You can find specialty paper in bright colors with glitter, lace details, or unique patterns to add that perfect finishing touch to your scrapbook. If you like creating your own greeting cards, pick up some paper packs so you have a large supply of the basic colors you need. Then you can choose specialty paper to add those small details that will make your cards more memorable. Shimmering, foil, and metallic papers are excellent for celebratory cards. If you're creating cards for kids, making your own designs on sticker paper will give them something enjoyable to play with along with the card. When you're searching for a great selection of specialty paper supplies to choose from for your next project, you'll find everything you need when you shop at HSN.


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e-SIDES Success Story: Beyond Privacy - Ethical and Societal Implications of Data Science
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© 2017 IDC Italy. Privacy Policy [email protected]
This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 731873. The views expressed on this website are the sole responsibility of the authors and do not necessarily reflect the views of the European Commission. Copyright belongs to the authors of this website. Use of any materials from this website should be referenced and is at the user's own risk.


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Tag Archives: Richmond Progressive Alliance
National Lawyers Guild Letter to KPFA On The Morning Mix
Posted on August 13, 2014 by webweaver2
REMOVAL OF MORNING MIX FROM DRIVE TIME PROGRAMMING
The recent removal of the Morning Mix radio program from the 8:00 AM time slot on KPFA has raised some concern at the San Francisco chapter of the National Lawyers Guild ("Guild"). We write this letter because KPFA and its free speech mission, are important to the Guild and to many activists that either work with, or are represented by, Guild members.
The Guild views KPFA not as simply another movement organization, but as a key part of the information commons. In that sense, KPFA is similar to a public utility — it is for the public benefit. KPFA policies on openness and actions regarding access to its airwaves affect all of us striving for a better world.
Like KPFA and Pacifica, the Guild was created with a particular mission: it was founded in 1937 as an alternative to the American Bar Association's exclusionary practices and political orientation, and the Guild was the first integrated bar association. KPFA was launched in 1949, three years after pacifist Lew Hill created Pacifica. The aim of the station has always been to promote cultural diversity, to promote pluralistic cultural expression, to contribute to a lasting understanding among diverse constituents, to maintain freedom of the press, and to create a forum for various viewpoints.
At KPFA's core is the concept of pacifism or non-violence. Non-violence is often mistaken for being simply the absence of, or opposite of, violence. Instead nonviolence is a systematic framework of both conceptual principles and pragmatic strategies to reduce harm and promote positive peace at the personal, community, national and global levels. Contrary to popular belief, non-violence requires boldness and courage. Moreover, it is easy to fall astray from the path of non-violence in the pursuit of financial stability or in response to political pressure.
With this framework and history in mind, we raise our concerns about an uncomfortable pattern of events that have transpired at KPFA that appear to be the antithesis of non-violence. We do not list these concerns to cast blame, or to impose our set of values on another organization. We list these concerns because our collective silence could be perceived as approval or consent. We consider individuals and organizations on both sides of this debate as both friends and allies. It is in the spirit of a friend and ally that we speak about the recent decisions at KPFA, and seek to build trust through transparency.
The Morning Mix was unique within the KPFA lineup because it was hosted by a diverse group of community volunteers with programming important to community members. The Morning Mix often reported on local political movements that were under-reported elsewhere. One such issue is tar sand extraction and transportation by rail to refineries. Andres Soto, one of the hosts of the Morning Mix, and a Richmond resident and activist, often reported on this issue. He frequently reported on Chevron's efforts to refine tar sands in Richmond which will have a direct impact on the people of Richmond and surrounding communities. Across the nation, we see a growing movement on this issue, and the Guild has recently received reports of brutal arrests of people who oppose tar sands. Instead of supporting this excellent reporting done by Andres Soto on this issue, KPFA has essentially silenced him by eliminating the prime time Morning Mix program. It is doubtful that the new paid host from LA will report on local efforts to oppose refining tar sands in the same way.
We could go through other hosts and programs on the Morning Mix, and discuss how each is connected to a local community and movement, however the point is that KPFA's actions have actually decreased the diversity of speech on its airwaves.
As a community-based radio station dedicated to pluralistic expression, it would seem that KPFA would wish to avoid even the appearance of decreasing diversity, or of favoritism, or of bias. Gentrification of a neighborhood transforms it by displacing local residents, which in turn erases local character. Defenders of gentrification support the transformation, claiming that it increases public safety. Some at KPFA have described the removal of the Morning Mix as a " move towards professionalism". However we fear that "professionalism", like "public safety" is pretext. The unqie character of the Morning Mix came from its local voices, accents, topics and perspectives. KPFA erased this local character with a single paid host out of LA.
Another reason put forth by by KPFA management is that the LA program will allegedly bring in more revenue. Although people can and do argue about interpretation of financial figures, the financial documents produced at the KPFA Local Station Board show that the Morning Mix was pulling is weight during fund drive. Thus, KPFA's reliance on a specific interpretation of its financial figures, when there are other valid interpretations, is a factor that creates the appearance of viewpoint bias. For example, the KPFA financial documents do not take into account the expenses incrred by having paid hosts. Thus, the financials purport to measure programs in terms of revenue generated, and disregard specific costs incurred by having paid hosts.
Moreover, and this point cannot be emphasized too much, KPFA can not and must not base all of its programming decisions on finance alone.
Although this letter was prompted by the removal of the Morning Mix, in the course of drafting this letter, we have learned of complaints that KPFA management has silenced specifically black programmers and/or failed to provide support for critical black programming or programming on critical local issues relevant to black communities. We are concerned that the removal of the Morning Mix, a show frequently hosted by black local hosts, is part of this pattern. We understand that KPFA is filling the Morning Mix time slot with a show hosted by a person of color, however the show is not produced locally, and does not have as close a connection to Bay Area black communities, and that features voices of black programmers, and not assume that programming by or for people of color generally will necessarily cover these issues.
KPFA, as part of its mission, must be ever vigilant of protecting diversity of viewpoints. Removal of the Morning Mix has narrowed the range of speech on its airwaves.
KPFA appears to promote radio programs that would prefer to talk about global economics, rather than race and the local displacement of black and immigrant families. It is an agenda that appears it would rather talk about gender discrimination in the boardroom, but not talk about the impact of gender, race and poverty on the young girls caught up in sex trafficking on Bay Area streets. It is an agenda that appears it would rather solve problems abroad, rather than those at home.
The Guild is an organization dedicated to human rights over property rights, and our collective conscious is touched when KPFA – a radio station dedicated to promoting diversity – consciously or unconsciously engages in viewpoint suppression. The allegations may be uncomfortable, however we in the Guild believe that it is through transparency and discussion of diverse viewpoints that this situation can be resolved.
Sharon Adams, Vice President
National Lawyers Guild, Bay Area Chapter
NLG letter re Mix & KPFA
Posted in Analysis, Announcement | Tagged Andres Soto, Anthony Fest, chevron, davey d, hard knock radio, kpfa, kpfk, Mickey Huff, morning mix, national lawyers guild, NLG, pacifica, Peter Phillips, Project Censored, Richmond Progressive Alliance, Sabrina Jacobs, Sharon Adams, Sonali Kolhatkar, steve zeltzer, tar sands, uprising, work week
Chevron, the Richmond City Council and the Morning Mix
Chevron's freedom to pollute vs. Bay Area residents' right to breath
by Daniel Borgström
On Tuesday, July 29th, I went to the Richmond City Council meeting where the council was to make a decision on a proposed expansion of the Chevron Refinery. The City Planning Commission approved the expansion, but with conditions that Chevron didn't want to accept. So Chevron appealed it to the City Council.
It was held in the large Richmond Auditorium to accommodate an expected crowd of Bay Area residents (and paid-by-Chevron speakers), 15,000 of whom were sent to the hospital following the huge refinery explosion in 2012. Chevron mobilized several hundred employees to attend the meeting, wearing blue and white pullover shirts, and waving signs saying "A Modernized Refinery" and "Richmond Proud" — slogans from Chevron's PR campaign. The blue & white shirts made their supporters very visible, and at first it appeared that they overwhelmingly outnumbered people of the Richmond Progressive Alliance (RPA).
The RPA was indeed outnumbered, but not as badly as it had at first appeared. Judging from the amount of applause that speakers from each side received, I could tell that there were a sizable number of people there to support the RPA or who supported their position.
For the past two decades, the RPA has been standing up to Chevron, which has always dominated Richmond. At this hearing the RPA called for the City Council to affirm the Planning Commission's conditions to impose environmental standards and limit pollution.
There were about 80 speakers. A friend and I stayed only for the first two hours. Most of the speakers during this time expressed concern about air quality and health problems; these included Asian community members who had been hospitalized as a result of inhaling toxic fumes during the refinery fire. Some of the refinery's critics wore signs saying: "I'm not paid to be here." — that was in reference to reports that Chevron supporters at the previous meeting had been paid to attend. A reporter from KPFA found a woman with a clipboard checking off names of Chevron's acolytes. The clipboard lady of the previous week was also at this meeting. Another KPFA reporter got a photo of her.
The people sitting around us included people from both sides. Interestingly, several times I noticed some of the people in blue and white applauding speakers who pointed out the environmental hazards created by the refinery. That surprised me; I didn't know what to make of it, or what it might imply.
Canadian activists block highway to Chevron refinery to protest Chevron's participation in the Pacific Trail Pipeline and the destructive gas fracking it proposes using to supply the pipeline to the coast.
We left at about 8:30 p.m., before the city council made its decision. Afterwards I heard the news, that the council acceded to Chevron's demands. Mayor Gayle McLaughlin and Vice Mayor Jovanka Beckles abstained over the failure to fund the hospital which had treated people during the 2012 Chevron fire.
Richmond has been a company town throughout its existence. First it was a Standard Oil town. When Standard Oil was broken up, it became a Chevron town. During the 1980s and 90s it spread less money around, probably because of corporate tax breaks making it less tax wise, and that made an opening for the RPA. When the RPA made gains and Chevron realized they'd lost control, Chevron began a campaign which included spreading money around as part of a "community benefits" agreement — one way that Chevron gets nonprofits on their side.
It left me wondering if Chevron might've also invested some of its PR budget money in KPFA, encouraging the clique who run the station to take Andrés Soto off prime time. Andrés had been a very effective show host of KPFA's Morning Mix; and an RPA activist with Communities for a Better Environment. He often focused on news about the Richmond refinery and its environmental effects — the 2012 refinery explosion and resulting pollution which sent 15,000 people to hospitals, as well as the hazards of the dirty crude which was being brought into the town in railroad tank-cars. He was also tuned into Chevron's affect on Richmond politics and talked about who is in Chevron's pocket. Andrés Soto's show is hardly something that Chevron would care to have broadcast across Richmond as they try to reclaim it as the company town it was before the rise of the RPA
Ann Garrison and Steve Gilmartin contributed to this article.
To read more from Daniel Borgstrom:
http://danielborgstrom.blogspot.com/
Andrés Soto's program, now titled "Afternoon" can be heard from 3:30-4 pm on Thursdays at KPFA, 94.1 fm, or streaming at kpfa.org. His program was cut in half and given a more obscure time slot when the Morning Mix was taken off the air..
Posted in Right Sidebar | Tagged chevron, Daniel Borgstrum, environmental hazards, Mayor Gayle McLaughlin, Richmond Progressive Alliance, Vice Mayor Jovanka Beckles
Green Party of Alameda County Signs on to SF Green Party Statement to "Report Locally"
Posted on July 13, 2014 by webweaver2
The Green Party of Alameda joins the San Francisco Labor Council, the Gray Panthers,ILWU Local 10, East Bay Veterans for Peace,Sonoma County Veterans for Peace, ILWU Local 10, the Harvey Milk LGBT Democratic Club, the Richmond Progressive Alliance, the San Francisco Green Party and the Golden Gate Letter Carriers in calling for restoration of the KPFA Morning Mix to its 8 am weekday hour.
"Think globally, act locally" is as relevant today as it was in 1915, when Scots biologist, sociologist, and town planner Patrick Geddes wrote Cities in Evolution. "We need locally produced, locally relevant programming to help us make specific connections between our daily lives and politics and those of the international community and the planet."
We find it difficult to understand why you replaced The Morning Mix with syndicated programming produced in Los Angeles, because locally produced programming about politics, art, culture, and the environment in a station's fm signal area is the heart of community radio. We need to understand the realpolitik immediately around us, in the San Francisco Bay Area, not just in Iraq, the Ukraine, Nigeria, Los Angeles, or the distant chambers of Washington D.C. or the United Nations.
In the San Francisco Bay Area, the movement towards community-based and/or regional renewable power infrastructure has reached a critical stage. We need to understand every step forward or backwards as this story unfolds on the ground, in our City Council and County Board of Supervisors offices, in public agencies and at public gatherings. San Franciscans need to know what is happening in the City of Richmond, in Marin, Sonoma, and Napa Counties, and in East Bay and South Bay counties where citizens are attempting create renewable energy infrastructure.
Despite a California State mandate to produce at least 20% renewable power by 2010, PG&E is still producing only 19%, four years later, and doing whatever it can to stop Bay Area communities from creating clean energy buyers' co-ops, or banding together as one and eliminating its dirty energy monopoly. PG&E strategists may have been most successful at the San Francisco Public Utilities Commission, where they have used the San Francisco Mayor's office – which they traditionally control – to block the implementation of our renewable power plan Clean EnergySF for two years, even after the San Francisco Board of Supervisors unanimous vote for it.
PG&E has also been able to activate its union, the International Brotherhood of Electrical Workers 1245, to oppose CleanPowerSF; this calls for the attention of a local labor reporter like Morning Mix host Steve Seltzer.
Uprising host Sonali Kolhatkar lives within Southern California Edison's monopoly and cannot possibly cover this as our local hosts can. We need diverse voices of hosts and reporters in touch with those on the ground, not the lone voice of Brian Edwards-Tiekert and/or his pinch hitter, Marie Choi, much as we appreciate the addition of Marie's voice to the morning hours.
This is not a "narrowly focused, local issue," as KPFA Interim General Manager Richard Pirodsky suggested the Morning Mix hosts had typically covered. in his parting lecture to the KPFA Local Station Board. We're thinking globally and acting locally, for the survival of the planet and a sustainable peace rather than never-ending dirty energy wars. The same can be said of efforts to create municipal and regional mass transportation networks,local agriculture, just criminal justice, and other central elements of sustainable culture.
Every municipality in the Bay Area struggles with criminal justice issues including racial profiling, police brutality, police accountability, whether or not to arm police officers with tasers, whether to allow stop'n frisk, whether to allow Police Departments to report juveniles to immigration authorities, and police shootings of minority youth like Oscar Grant, Alan Blueford, Alex Nieto, and Andy Lopez. These police issues are all part of a national discussion, but local decisions determining how they play out here are made at multiple local levels every day. .
What does an LA or New York broadcast host know about the San Francisco Re-entry Council, which created a model for re-integrating ex-offenders that is now studied nationally? What do they know about former San Francisco Sheriff Mike Hennessey, current Sheriff Ross Mirkarimi, and Public Defender Jeff Adachi's groundbreaking work in rehabilitation and re-entry?
How much can they know about Oakland's infamous police corruption or the Oakland Domain Surveillance Center proposed barely a year after Occupy Oakland grabbed the national and international stage?
How much can they know about the Richmond Progressive Alliance and Contra Costa County's struggles with the Chevron refinery, crude-by-rail shipments, and expanding oil infrastructure?
Citizens are working to stop potentially explosive crude-by-rail shipments from the Bakken Shale all over the U.S. and Canada, but shouldn't we be specifically informed about the crude-by-rail shipments threatening our own communities here? If not for KPFA Morning Mix host Andrés Soto and the Richmond Progressive Alliance, many residents of the Bay Area might not even realize that crude-by-rail shipments now threaten their own communities, not just Contra Costa County's.
This may not be of concern to KPFA's wealthier subscribers who never have and never will have to live next to an oil refinery, a crude-by-rail transit line, an oil storage tank, or any of the radioactive and otherwise toxic sites that the U.S. Navy abandoned all around San Francisco Bay. They may never have to face any number of other injustices in their daily lives, but if KPFA is to foster real community within the fm signal area it claims to serve, in accordance with its mission, it must consider these injustices to some as injustices to all. It must not exclude them from the station's early morning hours.
On July 12, 2014, the Green Party of Alameda signed on this statement.
Posted in Announcement | Tagged Andres Soto, davey d, kpfa, kpfk, kpft, labor fest, morning mix, pacifica, Project Censored, radio, Richmond Progressive Alliance, Sonali Kolhatkar, uprising, wbai, wpfw
Veterans for Peace Sonoma County Supports the Morning Mix in Prime Time
Posted on June 19, 2014 by webweaver2
From Bill Simon, PhD
President, Veterans For Peace Chapter 71, Sonoma County
Statement: on KPFA
Sonoma County Veterans for Peace supports the continuation of the Morning Mix at KPFA in prime time hours. The Morning Mix has been on KPFA at 8:00 A.M. for three and half years. They are men and women; black, white, and brown; and are gay and straight; radical scholars and labor activists; young, old, retirees, and are all volunteers in service to the mission of KPFA. We strongly support this type of community programming instead of a daily external show from LA.
Posted in Announcement | Tagged Andres Soto, Anthony Fest, Bernard Duncan, Dan Siegel, davey d, Jose-Luis Fuentes, kpfa, kpfk, Margy Wilkinson, Mickey Huff, morning mix, pacifica, Peter Phillips, Project Censored, richard pirodsky, Richmond Progressive Alliance, Sabrina Jacobs, Sonali Kolhatkar, steve zeltzer, uprising, veteransfor peace, wbai, wpfwm kpft
Harvey Milk Democratic Club Passes Resolution To Restore The Morning Mix
On June 17th, San Francisco's Harvey Milk Democratic Club adopted a resolution calling for the return of the Morning Mix to KPFA's 8am time slot, Mondays to Fridays.
Posted in Announcement | Tagged Andres Soto, Anthony Fest, davey d, Mickey Huff, morning mix, Peter Phillips, Project Censored, Richmond Progressive Alliance, Sabrina Jacobs, Sonali Kolhatkar, steve zeltzer, uprising


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Obama: Court made 'mistake' on VRA
Obama said the court underestimated the problem of voter supression. | AP Photos
By Jennifer Epstein
President Barack Obama on Thursday welcomed the Supreme Court's rulings on same-sex marriage, but said the high court "made a mistake" in its decision to overturn a key piece of the Voting Rights Act.
Speaking from Dakar, Senegal, in his first remarks since those decisions were handed down earlier this week, Obama said he would push forward to respond to the implications of both issues.
On marriage, Obama said he believes that the unions performed in one state should apply in another and should make those couples eligible for all the federal benefits afforded to married couples. "It's my personal belief — and I'm speaking now as a president [not] as a lawyer — if you're married in Massachusetts and you move someplace else, you're still married," he said at a news conference with Senegalese President Macky Sall.
"But again, I'm speaking as a president and not as a lawyer," he cautioned, saying that lawyers in his administration are working out the details of what Wednesday's Supreme Court rulings will mean.
( PHOTOS: President Obama in Africa)
That work is being done by the executive branch in a "systematic and prompt way," he said. "It's important that people who deserve these benefits, that they're getting them quickly."
The Supreme Court's decision Wednesday overturning a key piece of the Defense of Marriage Act was "not simply a victory for the LGBT community, I think it was a victory for American democracy," the president said, following up on a written statement he made from aboard Air Force One.
( PHOTOS: Reactions to Supreme Court's gay marriage rulings)
"I believe at the root of who we are as a people, who we are as Americans is a precept that we are all equal under the law," he said, and the high court's decision is "one more step towards ensuring that those basic principles apply to everybody."
Obama said speaking Wednesday to Edie Windsor, the plaintiff in the DOMA case, was a "special" moment, given that all she and her late wife had gone through in their 40 years together. "And that was just a microcosm of what it meant to families and their children all across America," he said.
( Also on POLITICO: Obama unlikely to push gay marriage)
But with its ruling on the VRA, the Supreme Court "made a mistake," Obama said. The high court "didn't recognize the degree to which voter suppression is still a problem around the country, and that it makes sense for us to put in place mechanisms to check practices and procedures that may make it difficult for people to vote in those areas where there's been a history in the past of discrimination."
While Congress can't overturn the ruling, "there are other potential remedies" to make sure people are able to vote. Lawmakers, he said, should consider legislation that says that "regardless of where you are, regardless of where you live, there are going to be certain rules that apply to elections."
Obama also defended his approach to the case of Edward Snowden, the leaker of classified information about National Security Agency surveillance programs.
( Also on POLITICO: The DOMA decision ripple effect)
Though some critics have cast him as weak for being unable to persuade the Chinese and Russian governments to cooperate and extradite Snowden, Obama said the case — while fascinating to the press and many Americans — isn't consequential enough at this point to merit his muscle.
"I have not called President Xi personally or President Putin personally and the reason is because, No. 1, I shouldn't have to. This is something that routinely is dealt with between law enforcement officials in various countries and this is not exceptional from a legal perspective," he said. "No. 2, we've got a whole lot of business that we do with China and Russia and I'm not gonna have one case … suddenly being elevated to the point where I've got to start doing to do wheeling and dealing and trading on a whole host of other issues simply to get a guy extradited so that he can face the justice system in the United States."
Underscoring the relative unimportance of getting Snowden back, Obama later added: "No, I'm not going to be scrambling jets to get a 29-year-old hacker."
"The damage was done" with Snowden's leaks, the president said, and at this point, he's most interested in preventing similar incidents and in fostering a debate over the balance between security and privacy. Meanwhile, Russia and China "should be abiding by international law, and we'll continue to press them as hard as we can to make sure they do so."
Obama addressed the influence of former South African President Nelson Mandela, who is said to be in failing health. "He's my personal hero," he said. "But I'm not unique in that sense … he's a hero for the world. His legacy will linger on through the ages."
After wrapping up his visit to Senegal, Obama is headed to South Africa. The White House has said that the president will be sensitive to the wishes of the Mandela family in determining his activity there.
Barack Obama,
U.S. Supreme Court,
Defense Of Marriage Act,
DOMA,
Gay Marriage,


First Lady Lady Bird Johnson, always willing to help Keep America Beautiful, dedicated this rest stop on May 11, 1965, according to a plaque on a rock.
In the Dumfries Rest Area on southbound I-95 at Virginia milepost 156.
Lady Bird's Rock was recently painted a nice shade of blue!
Lady Bird Johnson, first lady of President Johnson, officially dedicated the Dumfries I-95 Rest Area in 1965. We're guessing, but this painted rock probably wasn't what Lady Bird had in mind when she set out on her campaign to beautify America's highways.
Iwo Jima Statue, Triangle, VA - 5 mi.
U.S. Marine Corps Museum, Quantico, VA - 6 mi.
Staff Sgt. Reckless, Marine Hero Horse, Quantico, VA - 6 mi.
Washington Never Slept Here, Washington, DC - 25 mi.


Interest rates on new credit card offers remained static Wednesday, according to the CreditCards.com Weekly Credit Card Rate Report.
The national average annual percentage rate (APR) remained at 14.95 percent, after falling the previous week for the first time in nearly a month.
Wells Fargo prompted last week's dip in rates by lowering the APR on its student credit card.
The move -- which was the first by Wells Fargo in months (at least among the cards tracked by CreditCards.com) -- barely dented the national average, pushing it down by just a hundredth of a percentage point.
Most credit card issuers have refrained from making significant changes to their offer terms for much of the past year.
Instead, many are choosing to selectively adjust offers on just a small number of cards. As a result, the national average hasn't moved below 14.9 percent since February 2012.
Most credit card issuers have also remained relatively conservative with their marketing efforts in recent months. For example, issuers dialed back the number of card offers they mailed to consumers in 2012 by nearly 40 percent compared to the previous year, according to research by Mintel Comperemedia.
Issuers' appetites for new customers may be increasing, however.
Issuers mailed 16 percent more offers in January 2013 than they did in December 2012, according to a research note released Feb. 25 by the financial services firm Credit Suisse, citing Mintel Comperemedia research. Compared to the same period in 2011, credit card mailings jumped an impressive 21 percent.
The double-digit leap in mail volume is significant, considering how flat credit card mail volume was for most of 2012.
After dropping precipitously in December 2011, mail volume fluctuated somewhat in early 2012, but remained exceptionally flat in the summer and fall. By the end of the year, Mintel Comperemedia research shows that credit card mail volume dropped by 38 percent in 2012 compared to 2011, according to a Jan. 22 research note by Credit Suisse.
When mail offers dropped, experts partly attributed it to a shift in marketing strategy. For example, rather than rely as heavily on mailing credit card offers to consumers' mailboxes, which can get expensive, many issuers are experimenting with other ways to reach new customers.
In addition, the feeble economic recovery in the U.S. and the ongoing fiscal uncertainty created by ongoing legislative battles over government spending and taxation also played a significant role in dampening issuers' appetites, experts say.
Consumer spending, for example, was relatively weak throughout 2012, with credit card debt unexpectedly dropping by more than 5 percent in the final month of the year, according to consumer debt research by the Federal Reserve. The unemployment rate, meanwhile, declined in 2012, but barely, beginning the year at 8.3 percent and ending it at 7.8 percent, according to the Labor Department.
Currently, both consumers and businesses are facing significant uncertainty over the impact that federal spending cuts, which as of press time are still scheduled to take effect, will have on the economy.
However, credit card issuers, at least, appear to be feeling confident enough in the overall direction of the U.S. economy that they're willing to hunt for new customers more aggressively.
"We believe that 2013 will see moderately increasing competition for revolving balances," wrote Credit Suisse analysts Moshe Orenbuch and Meredith Roscoe in a research note about last month's jump in credit card mailings. Already, competition between credit card issuers is strong, they say, especially when it comes to reaching out to cardholders with deeper pockets.
Consumers, meanwhile, are also feeling somewhat better about the economy as well -- at least for now.
Significantly more consumers reported feeling optimistic about the U.S. economy in February after reporting increased pessimism the previous month, according to a new report from the Conference Board, released Feb. 26.
"Consumer Confidence rebounded in February as the shock effect caused by the fiscal cliff uncertainty and payroll tax cuts appears to have abated," said the Conference Board's Lynn Franco in a statement. "Consumers' assessment of current business and labor market conditions is more positive than last month. Looking ahead, consumers are cautiously optimistic."


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Videogame (1983). Berserker Works (BW). Designed by Fred Saberhagen. Platforms: AppleII (1983); DOS (circa 1985).
In 1983 the science fiction editor Jim Baen founded not only the sf and fantasy publishing house Baen Books but also the less well known Videogame publisher Baen Software (BS). At this time the sf author Walter Jon Williams had been writing historical novels under the name of Jon Williams, and designing associated games – including the eighteenth century tabletop naval game Tradition of Victory (1978 Erisian Games) and its revision Privateers and Gentlemen (1983 Fantasy Games Unlimited) – variously as Walter Williams and Jon Williams. (Tradition of Victory includes both a Wargame, Promotions and Prizes, and a pen and paper Role Playing Game, Heart of Oak, both of which were included in Privateers and Gentlemen with some additional material.) Baen hired Williams to work as a game designer for his new software company. Meanwhile, the science fiction author Fred Saberhagen and his wife Joan had become intrigued by the potential of the then new medium of the computer game (an interest which is clearly visible in the text of Saberhagen's novel Octagon , inspired by the Play by Mail wargame Starweb ), and had founded their own development studio in 1982 with assistance from Baen. This was Berserker Works, intended to create games which used stories by Saberhagen and other sf writers as the raw material for experiments in Interactive Narrative. A number of interesting works were produced by this complex of interrelated companies and individuals, including an early Computer Wargame dealing with galactic conquest – Starclash II (1984 BS, DOS) designed by Stephen Walton – and the "Regency Romance" game Pride and Prejudice (circa 1984 BW, AppleII, C64, DOS) designed by Walter Jon Williams, in which players compete to win the affections of a wealthy bachelor in a scenario inspired by the novels of Jane Austen. Saberhagen designed several products derived from his own Berserker series, notably the Computer Wargame Berserker Raids (1983 BW, AppleII, Atari8, C64, DOS) – a game of space strategy created with Lloyd Johnson – and Sign of the Wolf (1987 ebook chap), an illustrated version of the short story "Sign of the Wolf" (May 1965 If) which was sold on a disk.


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The Guardian adds 'support us' message to advertising
The Guardian is kicking off a five-week ad campaign encouraging people to support the newspaper or subscribe to help its journalism call the powerful to account.
The work is designed both to spread the message that The Guardian is worth supporting and to drive new subscriptions or financial contributions to the newspaper and its digital offering.
Karmarama created a 30-second film, "A space for change", that aims to achieve the former objective by focusing on examples of Guardian reporting that has produced change, such as the treatment of Windrush immigrants and the Cambridge Analytica scandal.
The spot recalls the space device used in Karmarama's January campaign for the newspaper's change of format from Berliner to tabloid. A voiceover by actress Zawe Ashton states: "There is a space where the silenced are heard and governments are forced to listen… Our journalism can change the story, creating space for clarity, imagination, hope… It's a space worth supporting."
The Guardian's other agency, Oliver, contributed print, digital outdoor, social, programmatic display, search, email and retail activity to the overall campaign, which is called "Subscribe to change".
The campaign sees the loss-making publisher extend its financial support appeals, which have appeared on its website since 2016, to its advertising. The appeals have so far resulted in 570,000 members subscribing or making recurring payments, plus 375,000 one-off contributors.
Sonia Sudhakar, marketing director at Guardian News & Media, said: "This time, we are going beyond demonstrating the societal importance of our journalism and directly asking people to support us in our mission through the range of Guardian products and support points."
The film launches on 24 September and will run across independent cinema, video-on-demand, high-impact out-of-home formats, YouTube and high-impact owned channels. Media planning and buying is handled by PHD.
Sudhakar added: "I'm particularly happy about the great cross-agency collaboration and
new ways of working. Cross-team sprints helped us get to great integrated work quickly, being agile and brave, whilst staying true to our brand values and playing to our strengths."
Karmarama, Oliver and The Guardian's marketing team worked together in a creative "sprint" to come up with the concept and strategy.
Dan Rutherford, Karmarama's executive creative director, said the campaign showcases "why The Guardian is a space worth protecting", while Oliver creative director Sam Jacobs said it was "tightly integrated and spoke to the brand's purpose at all touchpoints".
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Expand your material handling capabilities with this attachment which turns your John Deere loader into a forklift. This set of pallet forks fits John Deere 600 to 700 series loaders. The 48" long Forks are 1 1/2" x 4" and have a lift capacity of 5,000 lbs. Perfect For Farming, construction, nurseries, landscaping, lumber yards, warehouses, salvage operations and more.


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Q: How to change highlight color in Jquery Mobile Select Option I have this select option

Is it possible to change the highlight color from skyblue to other color?
I'm using jquery.mobile-1.4.5.min.js/css
Note: I'm also trying to edit in developer tools but I can't find any editable element.

A: You should not do this.It is default behaviour of dropdown.There are some methods to do this.But these are not working in all browsers.
Better convert your <select> to <ul><li> format and do whatever you want.
Otherwise,use jQuery Mobile data-native-menu="false" property of dropdown :
<select id="selectID" data-native-menu="false">
  <option value="one">One</option>
  <option value="two">Two</option>
  <option value="three">Three</option>
  <option value="four">Four</option>
</select>

And use following css :
 .ui-selectmenu-list .ui-btn-active {
    background-color: green !important;
    border-color: green !important;
    }

A: Yes, the class you need to modify is ui-state-active
Ex:
.ui-state-active {
   background: red;
}

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