text:
\section{Introduction}

The phenomenon of electron positron pair production in the presence of an electric field was described quantitatively in the classic work of
 Schwinger \cite{Schwinger:1951nm}. He wrote down an expression for the probability of particle production
(per unit space time volume) by solving the Dirac equation  in a  uniform and constant background
electric field $E$ and obtaining the electron Green function. The expression is
\begin{eqnarray}
P (E,m) = 1-e^{-\Gamma V T}.
\end{eqnarray}
with
\begin{eqnarray}
\Gamma = {E^2\over 4\pi^3}\sum_{n=1}^{\infty} {1\over n^2}e^{-\pi m^2 n\over |E|}.
\end{eqnarray}

A noteworthy feature is that there is an exponential damping with the mass of the electron which signifies that it is a tunneling
phenomenon. Thus for laboratory electric fields the magnitude is negligible and unobservable.

Schwinger's derivation treats the electric field as classical and also ignores higher order effects such as the Coulomb force between the electrons. As shown in \cite{Semenoff} the presence of
the Coulomb potential modifies the solution for large values of the electric field. It is found that for $E>E_c$, (critical field), there is no potential barrier and hence no exponential suppression.
In this approximation the potential has the form  $ 2m-Ed-{\alpha\over d}$ \cite{Semenoff}, where $\alpha$ is proportional to the electric charge.
  When
\begin{eqnarray}
 	\label{Ecrit}
E=E_c={m^2\over \alpha},
\end{eqnarray}

the maximum of the potential is zero and there is no barrier.

It is clear that this is non perturbative in $\alpha$. One can then pose the same question in ${\cal N} =4$ Super
Yang-Mills theory which is also in the Coulomb phase. Here in the planar strong coupling limit one can resort to
the AdS/CFT correspondence and get an exact answer.
Again one finds a critical electrical field \cite{Semenoff}.

This is also what one expects from string theory in flat space: An open string in an electric field is a quark-antiquark pair
in an electric field. When the force due to the electric field is stronger than the string tension,
the effective string tension becomes zero and one can expect unsuppressed production of quark antiquark pairs from the vacuum.
The signal of this is that the Dirac-Born-Infeld action becomes zero (and starts to become imaginary) at the critical electric
field.

One can ask whether this effect can be observed in condensed matter systems by its consequences on conductivity \cite{Sondhi}.
The effect of Schwinger pair production and its influences on conductivity was shown using
holographic calculations in \cite{Karch-metallic, Karch-Sondhi}. Probe branes representing flavor quarks were introduced in an
AdS-Schwarzschild  background and placed in an electric field and the conductivity
was calculated \cite{Karch1}.
Similar systems were also studied in \cite{Myers,Bergmann,Kundu}. The electric field induced conductivity was found to be a
non-linear function of the electric field, and more importantly the critical
field turns out to be zero\cite{Bergmann}. In the  bulk calculation the absence of a critical field can be traced to the warp
factors. For an arbitrarily small electric field the warp factors reduce the effective tension of
the string and at some value of the radial coordinate
$u=u^*$, the DBI action threatens to turn complex. It can be shown then that this unphysical behavior is resolved if one
assumes that a non zero current is induced. This current is present even at
zero temperature and can be attributed to the Schwinger effect without, however, any exponential suppression. In the boundary
theory this can be attributed to the strong coupling effects which reduce the
critical field to zero.\footnote{Naively, if one lets $\alpha \to \infty$ in (\ref{Ecrit}), $E_c\to 0$.}

 It has also been shown that this effect can be described in terms of an effective event horizon at $u=u^*$,
not in the bulk metric, but in the open string metric on the brane \cite{Kim,Sonner}. In fact many of the results derived for
black hole backgrounds, such as the proof of the fluctuation dissipation theorem \cite{Son-Teaney} can be shown to be
directly applicable in this situation also.

There are situations, such as the one described in the Sakai-Sugimoto model \cite{SakSug}, where the branes do not reach as
far as $u^*$. In this case this effect is not there and the material
is insulating even when there is an electric field
\cite{Bergmann}. For the boundary theory this implies that the quarks are too heavy and the strong coupling interactions
are not sufficient to remove the barrier.

In the case that there is no barrier (due to strong coupling effects), the pair production takes place ``classically'' i.e. no
quantum mechanical tunneling is involved. One doesn't really
need the Schwinger formula to calculate conductivity. This is the situation dealt with in the classical bulk calculations
of \cite{Karch-metallic,Sonner, Kundu}. However one can ask the question whether,
in the case where there is a barrier, as in the Sakai-Sugimoto model, where chiral symmetry breaking induces a quark mass
and puts it in an insulating phase \cite{Kundu},
one can really use the Schwinger formula to calculate the conductivity. Schwinger's calculation is a one loop calculation
and since the quarks circulating in the loop transform in the fundamental
of the color group rather than the adjoint, this is a $1/N$ effect - beyond the planar approximation. If one includes the
Schwinger correction (exponentially suppressed) to the Maxwell action
(as calculated in \cite{Urrutia}) this would induce
corrections to conductivity that is proportional to the electric field.

In this paper we address this question. The Maxwell action on the brane (which is the leading term obtained in expanding the
DBI action)
is modified by the addition of the one loop effective action, which in the presence of a background electric field has an
imaginary part explicitly. If one calculates conductivity using the Kubo formula,
from the Green's function, which can be evaluated by the usual AdS/CFT
prescription, one expects a non zero real part. Indeed this is what we find. Thus we can conclude that what was thought to
be an insulating phase actually has a small conductivity.

Whether this is large enough to be observable experimentally depends crucially on the mass of the fermion. In metals the
role of particle and anti particle is played by
fermionic excitations at the Fermi surface which is ungapped and one can expect such effects. In ordinary metals the dispersion
relation is non relativistic and the Schwinger formula would not be directly applicable although. Moreover external electric
fields are screened in metals. It has been suggested that  systems such as graphene one can look for this effect \cite{ACG}.
In graphene the electrons and holes are effectively massless at the "Dirac points" and obey a relativistic dispersion relation. Nevertheless
the density of states is small enough that screening effect is not strong.
Also the rate may be large enough to be measurable \cite{ACG}. The holographic calculation would then be applicable in a strong
coupling version of this.

Another interesting feature that arises in this calculation is that there are regions where the real part of the conductivity is
negative.
While this is unphysical ordinarily and would be a sign that the approximations are breaking down, this need not be so when there is
a background electric field, from which energy can be pumped into the system. Thus in semiconductor physics it is well known that,
 Gunn diodes and tunnel diodes display negative differential resistivity in the presence of large external fields. A holographic
calculation showing this phenomena has been done recently \cite{Nakamura1, Nakamura2, Nakamura-Ooguri}. Our main point of departure
is that we are
working in a region where the phenomenon is due to a one loop effect in the flavor brane in the bulk.

In supersymmetric BPS configurations of branes, the low energy action is fixed by the symmetries. However when supersymmetry is
spontaneously broken by finite temperature effects one can expect finite loop corrections. Loop corrections can involve open
strings with ($\mathcal{A}$) both ends on the flavor brane or ($\mathcal{B}$)
with one end on the flavor brane and one end on the colored brane.

In case ($\mathcal{B}$) the loop diagram
with an infinite number of massive modes running around the loop dualizes to a tree diagram involving closed string modes
connecting the flavor and color branes (see figure \ref{embed1}). One can see that they are of $O(\lambda)$.
These are the same class of diagrams that generate the AdS background in the first place. So the question arise as to
whether we are double counting. Are these diagrams (of type ($\mathcal{B}$)) to be considered or are they already included when the
flavor brane is placed in an AdS space? In general it is the the UV limit of the open string loop that is reproduced by the
graviton tree diagram. The finite part of the open string loop requires all the massive closed string tree diagrams.
This continues to be true in the decoupling limit taken for the AdS/CFT correspondence. On the open string side, on the brane,
in the $\alpha '\to 0$ limit  only the massless open string particles traverse the loop. However the closed string side still requires
the full string theory  and the massive modes also contribute and their effect survives in this limit \cite{SarkSath}.\footnote{ In some situations the massive mode
contributions cancel and the duality holds for the massless modes on both sides\cite{SarkSath}.}  Thus one is tempted to conclude that
one has to explicitly calculate the finite part of a gauge theory loop diagram (with colored particle in the loop) on the brane placed in
 an AdS background.
The finite contribution  in the presence of an electric field has an imaginary part corresponding to Schwinger
pair production.  In situations where the open string metric develops a horizon  such effects are seen, in the gravity dual,
already at the tree level on the brane. But in general it is hard to imagine how an imaginary part can develop in an effective action except
 through loop effects. We leave the issue of type ($\mathcal{B}$) diagrams as an open question for the moment.

  However
diagrams of type ($\mathcal{A}$) are not included in the dual picture and must be computed - they are of order $\lambda  \times {1\over N_c}\times N_f$.  As an example if we
have two flavor branes separated by a small amount, we have $SU(2)$ broken to $U(1)$. The effective action for the $U(1)$ photon
will get corrected by the loop with $W^\pm$ or its fermionic partners running around.  This kind of symmetry  breaking occurs for
instance in the holographic description of strong coupling BCS theory \cite{KSSS}.

The actual calculation of these classes of diagrams is not very different - they differ only by an overall numerical factor which is of $O(N_c/N_f)$. Furthermore while the original Schwinger calculation involved only fermions in the loop in the supersymmetric theory there are fermions as well as bosons. The expressions for arbitrary spin are available in the literature \cite{Semenoff}. In this paper we are interested in probing the qualitative effects of the Schwinger effect, so we restrict ourselves to the fermionic contribution.

\begin{figure}[h]
 \centering
 \mbox{\subfigure[]{\includegraphics[width=3.5 cm]{31.eps}}
 \quad
 \subfigure[]{\includegraphics[width=3.5 cm]{4.eps} }
  \quad
 \subfigure[]{\includegraphics[width=4.5 cm]{32.eps} }}
 \caption{Figure (a) and (b) describe the tree level and the one loop diagrams (type $\mathcal{A}$) respectively for open string.
Figure (c) shows a
 a one loop diagram with one end of the open string on the colored brane (type $\mathcal{B}$). This dualizes to a closed string tree diagram.}
 \label{embed1}
 \end{figure}

Having discussed an overview and the motivation for our holographic study of Schwinger pair production in strongly coupled system,
here we briefly mention about the specific strategies we follow in the subsequent sections. Our aim is to
capture the effect of pair production process on the electrical conductivity in the context of Sakai-Sugimoto model.
In section (\ref{one}), we briefly discuss the holographic aspects of Sakai-Sugimoto model.
The bulk gravity theory of Sakai-Sugimoto model is built on the consideration of $N_f$ number of flavor $D8/\bar{D8}$ branes
probing the near horizon geometry of type IIA supergravity background corresponding to the $N_c$
number of color $D4$ branes. Using the
$D4-D8-\bar{D8}$ brane picture, we describe how the model holographically allows a deconfined boundary phase with broken
chiral symmetry.
In section (\ref{two}), we study the response of the Sakai-Sugimoto model to a constant electric background by turning it on
inside the world volume of the probe $D8/\bar{D8}$ brane. The DBI action of the
 probe $D8/\bar{D8}$ brane is modified accordingly. Moreover, we systematically
consider some time dependent fluctuation over the constant electric background and construct the associated effective classical
Lagrangian as a leading Maxwell term in the $\alpha'$ expansion of the modified DBI action. Our aim is to add an one-loop
effective action to this classical Maxwell action and study the gauge field dynamics governed by the total action.
It is important to mention that the quantum action we are interested in can be obtained by systematically covariantizing the one in
four dimensional flat space time. Therefore to accommodate
the quantum action we need to dimensionally reduce the classical action to a four dimensional subspace of the
$D8/\bar{D8}$ world volume.
The systematic recipe for adding the one loop effective Lagrangian capturing the physics of Schwinger pair production is
described in section (\ref{three}). The Schwinger pair of our interest is the quark antiquark pair
associated with end points of the fundamental string joining either $D4-D8/\bar{D8}$ or $D8-\bar{D8}$ brane stacks (modulo the comments of the previous paragraph).
Furthermore, in section (\ref{four}) by analyzing the quantum corrected effective Lagrangian,
we demonstrate the holographic method to compute the conductivity in the strongly coupled
boundary theory. For the conductivity computation we require the information of retarded Green's function.
In this work we calculate the Green's function using numerical methods.
Finally we plot the real part of the conductivity with the frequency of the fluctuating gauge field.
We summarize our results and conclude with some remarks on our analysis in section (\ref{five}).

\section{Sakai-Sugimoto model} \label{one}
Sakai-Sugimoto model provides a very successful holographic method to construct the type
IIA supergravity background, dual to the large $N_c$ QCD theory \cite{SakSug}.
The IIA background includes a stack of $N_c$ color $D4$ branes wrapping a $S^1$ circle.
In addition to that, within probe approximation, $N_f$ number of flavor $D8/\overline{D8}$
branes at two different points on the circle are also considered, accounting no back reaction on the $D4$ geometry.
The four dimensional boundary theory
of the $D4$ branes is realized as a QCD-like theory
with the $ N_c$ colors of gluons and the $N_f$ flavors of massless chiral fermions ($N_f \ll N_c$) with anti-periodic
boundary condition. The left (right) handed fermions come from the
spectrum of $D8(\overline{D8})$ flavor branes and they transform in the fundamental representation of both the color gauge group
$U(N_c)$ and the flavor gauge group $U(N_f)_L\times U(N_f)_R$. The above realization of the Sakai-Sugimoto model
is valid at a energy scale far below the Kaluza- Klein mass scale.

In more detail, we consider the near horizon limit of the
$D4$ branes in the type IIA string theory.
If we set the curvature of space time $R = {(\pi g_s N_c)}^{1/3} l_s = 1$ and impose the limit $N_c >>1$,
the metric structure takes the following form,
\begin{eqnarray}
ds^2 = u^{3/2}(- dt^2 + dx^2 + dy^2 + dz^2 + f(u) dx_4^2) + u^{-3/2}(\frac{du^2}{f(u)}+u^2 d\Omega_4^2), \nonumber \\
f(u) = 1-(\frac{{u_{KK}}^3}{u^3}), ~~ e^{\Phi} = g_s u^{\frac{3}{4}}, ~~F_4 = 3 \pi l_s^3 N_c d\Omega_4,
\label{back}
\end{eqnarray}
where $u_{KK}^{-1/2} = \frac{3}{2} R_4$ signifies the
supersymmetry breaking scale of the theory, $x_4$ is the circular direction with the periodicity,
$x_4 \sim x_4 + 2\pi R_4$ and $\Omega_4$ is the volume element of $S^4$.
The $(u, x_4)$ subspace turns out to be topologically a cigar. The tip of this $(u, x_4)$ subspace is localized at $u =u_{KK}$.
The $AdS/CFT$ correspondence maps this particular background (\ref{back}) to a
confined phase of the boundary gauge theory at zero temperature with the 't Hooft coupling parameter,
\begin{eqnarray}
 \lambda_{Sakai-Sugimoto} = 4 \pi g_s N_c l_s.
 \label{thooft}
\end{eqnarray}
Possible embeddings of $D8$ and $\overline{D8}$ probe branes consistent with the topology of the background (\ref{back})
correspond to the various chiral phases in the boundary QCD like theory. For example, one can construct a $\mathcal{U}$ shaped embedding
by smoothly joining the $D8$ and $\overline{D8}$ branes at
a radial distance $u_0 \geq u_{KK}$. The $\mathcal{U}$ shaped embedding holographically conceives a very
simple geometrical picture of the spontaneous breaking of
the chiral gauge group $SU(N_f)_R \times SU(N_f)_L$  to the diagonal one $U(N_V)$ \cite{SakSug}.
The form of $\mathcal{U}$ shaped embedding can be extracted by solving the equation of motion for $x_4$ obtained from the DBI action.
\begin{eqnarray}
 S_{D8}  =  -{\mathcal{T}}_8 \int d^9 X  e^{-\phi} Tr \sqrt{-\text{det}(\mathcal{G} +  2\pi l_s^2\mathcal{F})},
\end{eqnarray}
where ${\mathcal{T}}_8$ is the tension of $D8$ brane, $\mathcal{G} $ is the induced world volume of
metric and $\mathcal{F}$ is the world volume gauge field.
The boundary condition for the solution is fixed by specifying that the asymptotic separation between the
stack of $D8$ and $\overline{D8}$ branes at boundary is $L$.
Using the background metric (\ref{back}), the DBI action of $D8$ and $\overline{D8}$ stacks reduces to,
\begin{eqnarray}
 S_{D8} = - \mathcal{W} \int du ~u^4 ~{\Big[ f(u) {x'_4}^2 + \frac{1}{u^3 f(u)}\Big]}^{\frac{1}{2}}.
\end{eqnarray}
Here we have introduced the normalization constant $\mathcal{W}$ as follows,
\begin{eqnarray}
 \mathcal{W} = 2 N_f V_{\mathcal{M}_4} \Omega_4 {\mathcal{T}}_8,
\end{eqnarray}
where $ V_{\mathcal{M}_4} $ is the volume of 4-dimensional space-time $(t,x,y,z)$.
Finally the $\mathcal{U}$ shaped profile is obtained by solving the equation of motion for $x_4(u)$ coordinate.
 \begin{equation}
x_4'(u) = {1\over u^{3/2} f(u)} \left[{u^8f(u)\over u_0^8 f(u_0)} - 1\right]^{-1/2} .
\label{prof1}
\end{equation}
 A finite temperature extension of the confining phase can be holographically realized
by considering the Euclidean continuation of (\ref{back}). In the Euclidean signature, the time coordinate, $t^{E}$
develops a periodicity $t^{E} \sim t^{E}  + 1/T$,
where $T$ is identified with the temperature of the gauge theory. Moreover, the gravity background dual to the deconfined phase at finite
temperature is achieved with interchanging the role of $t$ and $x_4$ \cite{KS}.
In Minkowski signature, the corresponding black hole background reads as,
\begin{eqnarray}
ds^2 = u^{3/2}(- f(u) dt^2 + dx^2 + dy^2 + dz^2 +  dx_4^2) + u^{-3/2}(\frac{du^2}{f(u)}+u^2 d\Omega_4^2).
\label{backblack}
\end{eqnarray}
The background develops a horizon at $u = u_{T} = {(\frac{4 \pi T}{3})}^2$ and the blackening function is defined as,
\begin{equation}
 f(u) = 1- \frac{u_T^3}{u^3}.
\end{equation}
The induced metric of $D8$ and $\overline{D8}$ world volume becomes,
\begin{equation}
ds^2_{D8}= u^{3/2}(-f(u) dt^2 + dx^2 + dy^2 + dz^2 ) + u^{-3/2}\Big(\frac{(1+u^3 f(u) x_4'^{2})}{f(u)}du^2 + u^2 d\Omega_4^2 \Big).
\label{ind1}
\end{equation}
In this blackhole background, the $(u, x_4)$ subspace is topologically a cylindrical
and the possible embeddings of $D8/\overline{D8}$ brane
consistent with this topology turn out to the $\mathcal{U}$ shaped (broken chiral symmetry, $T < \frac{0.154}{L}$) and the parallel
embeddings (restoration of the chiral symmetry, $T > \frac{0.154}{L}$) \cite{SakSug}.
Again, both of them can be obtained from the DBI action with the boundary condition previously mentioned.
\begin{eqnarray}
 S_{D8} =  -\mathcal{W} \int du ~u^4 ~{\Big[ f(u) {x'_4}^2 + \frac{1}{u^3}\Big]}^{\frac{1}{2}}.
\end{eqnarray}

The form of $\mathcal{U}$ shaped embedding is fixed by the following equation of motion of the
$x_4$ coordinate,
 \begin{equation}
x_4'(u) = {1\over u^{3/2} \sqrt{f(u)}} \left[{u^8f(u)\over u_0^8 f(u_0)} - 1\right]^{-1/2} .
\label{prof2}
\end{equation}

\begin{figure}[h]
 \centering
 \mbox{\subfigure[]{\includegraphics[width=3.5 cm]{1.eps}}
 \quad
 \subfigure[]{\includegraphics[width=3.5 cm]{2.eps} }}
 \caption{Here we show the embeddings of the $D8$ brane corresponding to appropriate boundary phases.
Fig (a) corresponds to a deconfined boundary phase with broken chiral symmetry. Fig (b) depicts a deconfined boundary phase
with chiral symmetry restored.}
 \label{embed}
 \end{figure}
The allowed parallel $D8/\overline{D8}$ embedding satisfies,
 \begin{equation}
x_4'(u) = 0.
\label{prof12}
\end{equation}
The transition between the chiral symmetry broken phase to the
chiral symmetry restored phase is first order. In the dual gravity theory,
the curvature of $D8/\overline{D8}$ brane plays the role of order parameter.
Following these holographic aspects of the
Sakai-Sugimoto model, in the next section we elaborate upon the response of the deconfined phase with broken chiral symmetry to an
external electric field.

\section{External electric field and the construction of effective Lagrangian}\label{two}
Recently in \cite{Bergmann}, authors have thoroughly studied the response Sakai-Sugimoto model to the external electric as well
as magnetic field. Without the loss of generality we consider the electric field is directed along $z$ axis.
The response to the external field is studied by turning on an Abelian component of the unbroken
$U(N_V)$ gauge field in the world volume of probe $D8/\overline{D8}$ brane.
\begin{eqnarray}
 \mathcal{A} = \frac{1}{N_f} tr \mathcal{A}_{N_V}.
\end{eqnarray}
In this analysis, assuming a current flowing along the direction of the electric field one can set
a suitable choice of ansatz as,
\begin{equation}
 \mathcal{A}_z = E t + \Xi(u),
\end{equation}
where $E$ is the constant electric background and $\Xi(u)$ is the time-independent
fluctuation encoding the holographic
notion of boundary current \cite{Karch-metallic}.
With the above choice of gauge field, the modified DBI action for the $D8/\bar{D8}$ brane embedded in the gravity
background dual to the
deconfined phase of finite temperature gauge theory, is given as
\begin{eqnarray}
 S_{D8} = -\mathcal{W} \int du u^4 \sqrt{(f(u){x'_{4}}^2 + \frac{1}{u^3})(1-\frac{e^2}{f(u) u^3}) + \frac{f(u)\xi'^2}{u^3}},
\label{actiond8}
\end{eqnarray}
where we have introduced the dimensionless quantities like $e = 2 \pi l_s^2 E$ and $\xi = 2 \pi l_s^2 \Xi$.

It is important to note that the DBI action does not
explicitly depend on the gauge field fluctuations. Therefore the equation of motion for $\xi$ evokes a constant of motion $\mathcal{J}$.
\begin{eqnarray}
 \frac{u f(u) \xi'}{\sqrt{(f(u){x'_{4}}^2 + \frac{1}{u^3})(1-\frac{e^2}{f(u) u^3})}} = \mathcal{J}.
\label{eomd8}
\end{eqnarray}
Using (\ref{eomd8}) and substituting $\xi'$ in terms of the constant of motion $\mathcal{J}$ in (\ref{actiond8}) we get,
\begin{eqnarray}
  S_{D8} = -\mathcal{W} \int du u^4 \sqrt{\Big(f(u){x'_{4}}^2 + \frac{1}{u^3}\Big)\Big(f(u)-\frac{e^2}{u^3}\Big)
  {\Big(f(u)-\frac{{\mathcal{J}}^2}{u^5}\Big)}^{-1}}.
\label{actiond81}
\end{eqnarray}
Moreover, by demanding the reality of the DBI action (\ref{actiond81}) the response coefficient like conductivity
is holographically computed in the boundary theory.
By integrating (\ref{eomd8}) with respect to $u$ and then taking the boundary limit, the result
gives the leading asymptotic behavior of the gauge field,
\begin{eqnarray}
2 \pi l_s^2 \mathcal{A}_z = e t  -\frac{2}{3} \frac{\mathcal{J}}{u^{\frac{3}{2}}},
\end{eqnarray}
where $\mathcal{J}$ can be physically interpreted as the conserved current associated with $\mathcal{A}_z$.
To obtain the $\mathcal{U}$ shaped embedding of $D8/\bar{D8}$ brane we solve
the equation motion for $x'_{4}$ derived from the DBI action (\ref{actiond8}).
 \begin{equation}
x_4'(u) = {1\over u^{3/2} \sqrt{f(u)}} \left[\frac{u^8f(u)(f(u)-\frac{e^2}{u^3}){(f(u)-\frac{\mathcal{J}^2}{u^5})}^{-1}}
{ u_0^8 f(u_0)
(f(u_0)-
\frac{e^2}{u_0^3}){(f(u_0)-\frac{\mathcal{J}^2}{u_0^5})}^{-1}}
- 1\right]^{-1/2}.
\label{prof3}
\end{equation}
It is straightforward to get an on-shell DBI action $S^{\mathcal{U}}_{\mathcal{J}\ne 0}$ by substituting the above solution into
(\ref{actiond8}).
However, in \cite{Bergmann}, it has been shown that the physically
favored configuration allows no current as the on-shell DBI action always satisfies
$S^{\mathcal{U}}_{\mathcal{J}\ne 0} > S^{\mathcal{U}}_{\mathcal{J} = 0}$,
where $S^{\mathcal{U}}_{\mathcal{J} = 0}$ can be constructed by setting $\mathcal{J} = 0$ in (\ref{prof3}) and then substituting it
back to (\ref{actiond8}).
Therefore, in the boundary theory the deconfined phase with broken chiral symmetry
turns out to be insulating.

In our work, we accomplish a holographic re-analysis of the
aforementioned boundary phase but with an explicit time dependence in the
gauge field fluctuation inside the $D8/\bar{D8}$ world volume.
For further computation, we consider an approximation that the generalization of the time independent gauge field
fluctuation into the time-dependent one will not modify the $\mathcal{U}$ shaped classical embedding for
$\mathcal{J} = 0$.
The field ansatz in the Minkowski signature we are considering reads as
\begin{equation}
\mathcal{A}_z =  E t + \tilde{\Xi}(t, u).
\label{ans}
\end{equation}
Using this time-dependent gauge field ansatz (\ref{ans}),
it is straightforward to write down the DBI action for the $D8/\bar{D8}$ brane. We will purposefully
factorize the action for our future convenience. In particular, we shall keep track of the electric field by redefining
 the term under first square root as the modified world volume metric and then derive the fluctuation Lagrangian.
\begin{eqnarray}
S_{D8}  &=& -\frac{2 N_f \mathcal{T}_{D8}}{g_s} \int d^9x ~u^{-3/4}\sqrt{-Det(\mathcal{G}+(\mathcal{E} +\tilde{\mathcal{X}}(t, u)))}  \nonumber \\
       &=&  -\frac{2 N_f \mathcal{T}_{D8}}{g_s} \int d^9x ~u^{-3/4} \sqrt{-Det(\mathcal{G} +  \mathcal{E} )}  \nonumber \\
&& ~~~~~~~~~~~~~~~~~~~~~~\times \sqrt{Det(1 +  \tilde{\mathcal{X}}(t, u)(\mathcal{G} +  \mathcal{E})^{-1})}.
\label{newaction}
\end{eqnarray}
In our notation, $\mathcal{G}$ is again the world volume metric tensor for the $D8/\bar{D8}$ brane. $\mathcal{E}$ and $\mathcal{X}(t, u)$
are the world volume field strength tensors for the constant background and the time-dependent fluctuation respectively.
The non-zero components of $\mathcal{E}$
are
\begin{eqnarray}
 \mathcal{E}_{tz} = -\mathcal{E}_{zt} = e,
\end{eqnarray}
whereas, the same for $\mathcal{X}(t, u)$ are
\begin{eqnarray}
 \mathcal{X}_{tz} = - \mathcal{X}_{zt}= \dot{\tilde{\xi}}(t,u),~~ \mathcal{X}_{uz} = - \mathcal{X}_{zu}= \tilde{\xi}'(t,u).
\end{eqnarray}

Similar to the time independent case, here we also introduce the dimensionless quantities,
$e = 2 \pi l_s^2 E$ and $\tilde{\xi} = 2 \pi l_s^2 \tilde{\Xi}$.
For small values of gauge field fluctuation, we expand the DBI action using the following matrix identity,
\begin{equation}
 \sqrt{Det(1+M)} = 1 + \frac{1}{2}Tr M + \frac{1}{8} ({Tr M}^2) - \frac{1}{4} Tr{(M)}^2,
\end{equation}
where $M$ stands for $\tilde{\mathcal{X}}(t, u)(\mathcal{G} + \mathcal{E})^{-1}$.
In this expansion, it is sufficient for our purpose to keep the terms up to the quadratic fluctuations.

Neglecting those terms which are either constant or linear in fluctuation, thus not contributing to the equation of motion
 and putting everything else together up to quadratic order we get the classical action for fluctuation,
\begin{eqnarray}
S_{\text{cl}} &=& -\frac{2 N_f \mathcal{T}_{D8}}{g_s}\int d^9 x~ u^{-3/4} \sqrt{f(u)u^{3/2}
(1-\frac{e^2}{u^3 f(u)}) {(u^{3/2})}^3 ~\frac{u^{3/2}}{f(u)}
 (\frac{1}{u^3}+f{x_4'}^2)
\mathcal{G}_{\Omega_4\Omega_4}}\nonumber \\
&&  \times  \Big(- \frac{{\dot{\tilde{\xi}}}^2}{2f(u)u^3{(1-\frac{e^2}{f(u)u^3})}^2} + \frac{f(u){\tilde{\xi'}}^2}{2u^3(1-\frac{e^2}{f(u)u^3})
(\frac{1}{u^3} +f(u){x_4'}^2)}\Big) .\nonumber \\
\label{eqn1}
\end{eqnarray}
Our aim is to write $S_{cl}$ obtained by expanding DBI action up to quadratic order of fluctuation
in a canonical four dimensional Maxwell form. The motivation for imposing the restriction on space time dimension comes from the
fact that at the end we aim to study the effect of Schwinger pair production on electrical conductivity in a strong coupling phase
by analyzing the dynamics of gauge field fluctuation governed by a quantum corrected action and the quantum contribution for the
action we are interested in is originally constructed in \cite{Urrutia} for four dimensional flat space time.
Therefore to successfully accommodate the quantum correction we need the above mentioned dimensional reduction.
To do so we proceed in the following way. First, by observing the factors under the square root in equation (\ref{eqn1}) we
make an ansatz for a modified induced metric $\mathcal{\tilde{G}}$.
This modified metric absorbs the extra factor coming due to the presence of constant electric background $E$
and reduces to the original one, $\mathcal{G}$
in the $E \rightarrow 0$ limit.
Then we execute a dimensional reduction
on the DBI action realized over nine dimensional world volume
coordinates ($t,x,y,z,u,\theta_1,\theta_2,\theta_3,\theta_4$) and write it as an effective action in four dimensional space time
($t,y,z,u$), where $\theta_i$'s are the
angular variables in $\Omega_4$. Finally we redefine the coupling parameter in the four dimensional effective action
in such a way the final expression takes the desired canonical form.
The ansatz for the modified modified induced metric $\mathcal{\tilde{G}}$ of our interest is set as,
\begin{eqnarray}
 \mathcal{\tilde{G}}_{tt} &=& (1-\frac{e^2}{f(u)u^3})\mathcal{G}_{tt}, \nonumber \\
\mathcal{\tilde{G}}_{ij} &=& \mathcal{G}_{ij} ~~~~~~~\forall i,j.
\label{modmet}
\end{eqnarray}
With this modified metric (\ref{modmet}), we re-write the $S_{cl}$ in (\ref{eqn1}) in the following way,
\begin{eqnarray}
 S_{\text{DBI}} &=&  -\frac{2 N_f \mathcal{T}_{D8}}{g_s}\int d^9 x~ u^{-3/4} \sqrt{-Det\mathcal{\tilde{G}}} ( \frac{1}{1-\frac{e^2}{f(u)u^3}})~~\frac{1}{2}
\{\mathcal{\tilde{G}}^{tt}\mathcal{\tilde{G}}^{zz} { \mathcal{X}_{tz}}^2 + \mathcal{\tilde{G}}^{uu}\mathcal{\tilde{G}}^{zz}
{ \mathcal{X}_{uz}}^2  \}. \nonumber \\
\label{eqn2}
\end{eqnarray}
Moreover, we perform the dimensional reduction from nine to four dimensions.
It is important to note that in
doing so we make another assumption that one of the spatial boundary coordinates is wrapped in a
circle and introduces another energy scale $< u_{KK}$.
For all subsequent part of this paper we restrict our analysis far below this newly introduced energy scale.
Redefining the coupling constant in a
suitable way we finally land up with a four dimensional effective action in a canonical Maxwell form.
\begin{eqnarray}
 S_{\text{Classical}} &=& -\int d^4x \frac{1}{g_s^{eff}} \sqrt{-Det{\mathcal{\tilde{G}}}_4} ~~\frac{1}{4} F_4^2,
\label{classical1}
\end{eqnarray}
where, $g_s^{eff} = \frac{g_s (1-\frac{e^2}{f(u)u^3})}{2N_f \mathcal{T}_{D8}V_{\Omega_4} V_x 4 \pi^2l_s^4 u} =
\hat{g}_s^{eff}\frac{1-\frac{e^2}{f(u)u^3}}{u}$.
${\mathcal{\tilde{G}}}_4$ is the four dimensional effective metric having non-zero diagonal element,
\begin{eqnarray}
 {({\mathcal{\tilde{G}}}_4)}_{t t} = {\mathcal{\tilde{G}}}_{t t}, ~~  {({\mathcal{\tilde{G}}}_4)}_{u u} = {\mathcal{\tilde{G}}}_{u u }, ~~
   {({\mathcal{\tilde{G}}}_4)}_{yy } = {\mathcal{\tilde{G}}}_{y y},  ~~    {({\mathcal{\tilde{G}}}_4)}_{z z} = {\mathcal{\tilde{G}}}_{zz}.
\label{modmet1}
\end{eqnarray}

Since $u$ has been chosen to have zero length dimensions, the running Yang-Mills coupling constant consistently turns out to be dimensionless.
The non-zero components of the four dimensional field strength tensor $F_4$ are the following,
\begin{eqnarray}
 {F_4}_{t z} = \dot{\tilde{\Xi}}(t, u), ~~~~  {F_4}_{u z} = \tilde{\Xi}'(t, u).
\label{4dimfield}
\end{eqnarray}
Up to this stage, we construct an effective Maxwell action for gauge field fluctuation around a constant electric background
in four dimensional subspace of  $D8/\bar{D8}$ brane world volume characterized by the modified metric
${\mathcal{\tilde{G}}}_4$. In the next section, we discuss how to add a four dimensional effective action arising from the one-loop
correction.

\section{Adding one-loop quantum correction} \label{three}
In this section we discuss how to add a consistent one loop effective action to the tree level canonical Maxwell action,
(\ref{classical1}) in four dimensional space time defined by $\tilde{\mathcal{G}}_4$.
Following the methodology of QED, we point out that the structure of quantum
action, $S^{Q}$ solely depends on the loop contribution arising from the vacuum polarization tensor $M_{\mu\nu}$,
generically prescribed as a two point correlator of the propagating
gauge field.
In this paper we consider the modification of gauge field propagation in vacuum up to one loop order. The modification is due to
relevant polarization tensor $M_{\mu\nu}$ encoding the process of virtual quark-antiquark pair creation.
In the presence of an external homogeneous electric field $E$, the polarization tensor develops an explicit
dependence on the respective electric
field and further restricts the vacuum dynamics. Motivated by Schwinger's seminal work \cite{Schwinger:1951nm},
there has been already an extensive perturbative as well as non-perturbative study to compute the
vacuum polarization tensor for the pair creation process in terms
of double parameter integral, including the presence of a background electromagnetic field in four dimensional Minkowski space
\cite{Urrutia, Tsai:1974fa, Tsai:1975iz, Baier:2007dw, Baier:2009it, Dittrich:1985yb, Karbstein:2013ufa}.

In this kind of computations the externally set vector parameters are the field vectors and the transferred four momentum vector
$k_{\mu}$. For the simplification of the computation it is always convenient to decompose the back ground space time
along the parallel and the perpendicular directions to the external field. Without the loss of generality we consider the
electric field is directed along $z$ axis.
The four dimensional Minkowski space time coordinates $(t, y, u ,z)$, can be grouped as $(t, z) \Rightarrow ||$, and
$(u, y) \Rightarrow \perp$. Subsequently, the metric can be decomposed in the following way,
\begin{eqnarray}
 \eta^{\mu\nu} =  \eta^{\mu\nu}_{||} + \eta^{\mu\nu}_{\perp},
\end{eqnarray}
where $||/\perp$ stands for $(t, z)/(y, u)$ respectively. Furthermore, the transferred four momentum can be decomposed as,
\begin{eqnarray}
 k^{\mu} =  k^{\mu}_{||} + k^{\mu}_{\perp},
\end{eqnarray}
With above consideration, following \cite{Urrutia},
the momentum space representation of the polarization tensor in the presence of a homogeneous external field can be expressed up to
one loop level as,
\begin{eqnarray}
M^{\mu \nu} &=& \frac{\mathcal{C}}{2}\int_0^{\infty} \frac{ds}{s}\int_{-1}^{1}\frac{dv}{2} e^{-is\phi_0} \frac{ w^{'}}{\sinh w^{'}} \Big[(\eta^{\mu \nu}k^2 - k^{\mu}k^{\nu}) N_0
+ (\eta_{||}^{\mu \nu}k_{||}^2 -  k_{||}^{\mu}k_{||}^{\nu}) N_1 +
  \nonumber \\
&& ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + \text{contact terms} \Big],
\label{vacpol}
\end{eqnarray}
where $\mathcal{C}$ is an overall normalization constant and the other parameters $\phi_0$, $N_0 $ and $N_1$ are defined as,
\begin{eqnarray}
  N_0 &= &\cosh w^{'}v -v \sinh w^{'}v  \coth w^{'},
\label{para1} \\
  N_1& = &2  \frac{\cosh w^{'} - \cosh w^{'}v }{\sinh^2 w^{'}} - N_0,
\label{para2}  \\
 s \phi_0 &= &   sm^2 + \frac{k_{||}^2}{2} \frac{\cosh w^{'} - \cosh w^{'}v}{z^{'}\sinh w^{'}}
+\frac{1}{4} s (1-v^2)k_{\perp}^2 ,
\label{para3}\\
w^{'}& = & q s E,
\label{para4}
 \end{eqnarray}
where $m$ and $q$ are the mass and charge of the flavor quark. The contact term  in (\ref{vacpol}) can be fixed by demanding the following two conditions,
\begin{eqnarray}
 k^2 = 0,  ~~~~~~~
\lim_{\substack{ k^2 \to 0 \\ E \to  0}} M_{\mu \nu} = 0.
\end{eqnarray}
The form of contact term turns out to be,
\begin{eqnarray}
 \text{contact term} = - (1-v^2)(\eta^{\mu \nu}k^2 - k^{\mu}k^{\nu}).
\label{contact}
\end{eqnarray}
The constraints , $k^2 = 0$ on the regime of transferred four momentum signifies that the derivation of the $M_{\mu\nu}$ is fitted
to on-the-light-cone dynamics.
There are other possible forms of contact term which can be derived on-the-light-cone. However we have observed that the symmetry of frequency
dependent conductivity due to the pair creation is heavily dependent on the form of contact term as it contributes to
the quantum action.
Moreover, the holographic realization of the linear response theory suggests that the real part of the frequency dependent conductivity should be
symmetric with respect to
the associated frequency. By accounting these two facts we fix the contact term contributing to the polarization tensor to the above form
and the one-loop action in momentum representation becomes,
\begin{equation}
{ \mathcal{S}}^Q = - \int \frac{d^4k}{{(2\pi)}^{4}} \sqrt{- Det\eta}  A^{\mu}(k)M_{\mu\nu} (k)A^{\nu}(-k),
\label{qlag}
\end{equation}
where $M_{\mu \nu}$ is specified by the equations (\ref{vacpol}), (\ref{para1}), (\ref{para2}), (\ref{para3}), (\ref{para4}) and
(\ref{contact}). Translating from the momentum representation to the space time
representation the quantum action simplifies into,
\begin{eqnarray}
{\mathcal{S}}^Q &=& - \frac{\mathcal{C}}{4}  \int d^4x \sqrt{-Det \eta} \Big[Tr ({(F_4)}_{||}.\eta_{||}.{(F_4)}_{||}.\eta_{||})( I_1)
\nonumber \\
&& ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + 2Tr ({(F_4)}_{mixed}.\eta_{||}{(F_4)}_{mixed}\eta_{\perp})(I_2) \Big],
\nonumber \\
\end{eqnarray}
where $F_4$ is the same second rank field strength tensor of propagating gauge field defined in (\ref{4dimfield}).
More specifically, ${(F_4)}_{||}$ / ${(F_4)}_{\perp}$
allows only those space time indices which signify the
parallel/perpendicular direction to the external homogeneous electric field. On the other hand, ${(F_4)}_{mixed}$ signifies that one of
its space time
indices belongs to $(t, z) \Rightarrow ||$ and the other one takes value in $(u, y) \Rightarrow \perp$. Furthermore, $
I_1$ and $I_1$ carry the information of the double integrals in the action.
\begin{eqnarray}
 \nonumber I_1 = \int \frac{ds}{s}\int \frac{dv}{2} e^{-i s \phi_0}  \frac{ w^{'}}{\sinh w^{'}}(N_0+N_1-(1-v^2)), \nonumber \\
I_2 = \int \frac{ds}{s}\int \frac{dv}{2} e^{-i s \phi_0}  \frac{ w^{'}}{\sinh w^{'}} (N_0-(1-v^2)).
\label{integralcouple}
\end{eqnarray}

However, we need to construct a one-loop quantum corrected action in the four dimensional curved space time denoted by
$\tilde{\mathcal{G}}_4$.  Covariantization is to be done by using Riemann normal coordinates (RNC)\cite{Pet,Eis}.
If we denote by $y^\mu$ the RNC, then one interprets $k_\mu$ as $-i {\partial \over \partial y^\mu}$.
Various powers of derivatives can be re-expressed in terms of covariant derivatives and  the curvature tensors.
If the radius of curvature of the space is large enough, then to a first approximation we can neglect the curvature terms.
This is what will be done in this paper.  In the large $N_c$ limit, we can consider only the leading term for simplification of our analysis.
\begin{eqnarray}
{ \mathcal{S}}^Q &=& -\frac{\mathcal{C}}{4}  \int d^4x \sqrt{-Det \tilde{\mathcal{G}}_4}
 \Big[Tr {(F_4)}_{||}.{(\tilde{\mathcal{G}}_4)}_{||}.{(F_4)}_{||}.{(\tilde{\mathcal{G}}_4)}_{||})( I_1) + \nonumber \\
&& ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2Tr ({(F_4)}_{mixed}.{(\tilde{\mathcal{G}}_4)}_{||}{(F_4)}_{mixed}{(\tilde{\mathcal{G}}_4)}_{\perp})(I_2) \Big], \nonumber \\
\label{covaction}
\end{eqnarray}
where we consider the contravariant components of the
metric tensor $\tilde{\mathcal{G}}_4$ and the covariant component of the field tensor $F_4$.
It is extremely difficult to evaluate the integrals $I_1$ and $I_2$ with full generality. One of the ways out is to constrain the
full
parameter space by imposing weak field approximation,
\begin{eqnarray}
 \frac{q E}{m^2} <<1.
\end{eqnarray}
Within this weak field approximation if we expand the r.h.s of (\ref{para3}) in the powers of $E$, the
leading order contribution becomes: (We are interested in the frequency dependence of the conductivity.
Currents are assumed to be time varying but uniform in space. So we set $\vec k=0$ and $ k_0 = \omega \neq 0$.),
\begin{eqnarray}
s\phi_0 = sm^2 +\frac{1}{48}q^2\omega^2 |{\mathcal{\tilde{G}}}_{00}| s^3 {(1-v^2)}^2E^2.
\label{phiapprox}
\end{eqnarray}
We can define a relevant dimensionless parameter $\lambda$ such that it takes both small and large numerical
values depending on the
magnitude of frequency and the intensity of the field.
\begin{eqnarray}
 \lambda = \frac{3}{2} \frac{q E}{m^2}\frac{w}{m}.
\end{eqnarray}
 Similarly, under same approximation
\begin{eqnarray}
 (N_0 + N_1-(1-v^2)) \frac{ w^{'}}{\sinh w^{'}} =    - \frac{1}{12} E^2 q^2 s^2 {(5-6v^2+v^4)},  \nonumber \\
(N_0-(1-v^2)) \frac{ w^{'}}{\sinh w^{'}} =   - \frac{1}{6} E^2 q^2 s^2 {(1-v^2)}^2.
\label{const1}
\end{eqnarray}
It is important to note that, weak field approximation does not make contradiction with large and small values of $\lambda$. In both
cases the leading contribution for the integral mentioned in (\ref{vacpol}) comes from $s<<1$ \cite{Tsai:1974fa}.

Plugging the results of (\ref{phiapprox}) and (\ref{const1}) in (\ref{integralcouple}) we get,
\begin{eqnarray}
 \nonumber I_1 &=&  - \frac{1}{12} E^2 q^2 \int \frac{dv}{2} {(5-6v^2+v^4)}  \int s ds  e^{-i s \phi_0(\omega)},
\label{i1} \\
I_2 &=&  - \frac{1}{6} E^2 q^2 \int \frac{dv}{2} {(1-v^2)}^2  \int s ds  e^{-i s \phi_0(\omega)}.
\label{i2},
\end{eqnarray}
Now we evaluate the integrals $I_1$ and $I_1$ within the weak field approximation. To do so, first we
work out the $s$ integrals by applying the standard integral representation of the known special function.
We introduce the variable $r$ and the parameter $\rho$ for simplification of the computation,
\begin{eqnarray}
 r = \frac{1-v^2}{4}\frac{w}{m}q E \sqrt{|{\mathcal{\tilde{G}}}_{00}|} ~~s,  \nonumber \\
\rho = \frac{4}{\lambda}\frac{1}{1-v^2}\frac{1}{\sqrt{{|\mathcal{\tilde{G}}}_{00}|}}.
\label{def}
\end{eqnarray}
With the above redefinition, the relation between the $s$ and $r$ can be written in a compact form,
\begin{eqnarray}
 s \phi_0 &=& \frac{3}{2}\rho (r + \frac{r^3}{3}) , ~~~~~~~s = {(\frac{3 \rho}{2 m^2})} r.
 \end{eqnarray}
Correspondingly the real and the imaginary part of the $s$ integral are successfully translated into respective components
of $r$ integral.
\begin{eqnarray}
 \int_0^{\infty} s ds  \cos{(s \phi_0)} &=&
\frac{1}{m^4} {(\frac{3 \rho}{2 })}^2 \int_0^{\infty}  r dr \cos(\frac{3\rho}{2}(r+\frac{r^3}{3}))
\label{intres1},\\
\int_0^{\infty} s ds  \sin{(s \phi_0)} &=&
\frac{1}{m^4} {(\frac{3 \rho}{2 })}^2 \int_0^{\infty}  r dr \sin(\frac{3\rho}{2}(r+\frac{r^3}{3})).
\label{intres2}
 \end{eqnarray}
Again a suitable change of variable $r = {(\frac{3 \rho}{2})}^{-1/3} p$, recasts the r.h.s of the equation
(\ref{intres1}) in the desired form.

\begin{eqnarray}
\int_0^{\infty}  r dr \cos\Big(\frac{3\rho}{2}(r+\frac{r^3}{3})\Big) &=& {(\frac{3 \rho}{2 })}^{-2/3}
\int_0^{\infty}  p dp \cos\Big({(\frac{3 \rho}{2 })}^{2/3}p +\frac{p^3}{3}\Big),
\nonumber \\
&=& \pi {(\frac{3 \rho}{2 })}^{-2/3} Gi'[{(\frac{3 \rho}{2 })}^{2/3}],
\end{eqnarray}
where $Gi[x]$ is the inhomogeneous Airy function/Scorer function satisfying the
following differential equation and the boundary conditions \cite{Gil}.
\begin{eqnarray}
 Gi''[x] -xGi[x] &=& - \frac{1}{\pi}, \nonumber \\
Gi[0] &=& \frac{1}{3} Bi[0] = \frac{1}{\sqrt{3}} Ai[0], \nonumber \\
Gi'[0] &=& \frac{1}{3} Bi'[0] = -\frac{1}{\sqrt{3}} Ai'[0], \nonumber \\
\end{eqnarray}
where $Ai[x]$ and $Bi[x]$ are the homogeneous Airy function of the first kind and the second kind respectively.
Integral representation of $Gi[x]$ is given as ,
\begin{eqnarray}
 Gi[x] = \frac{1}{\pi} \int_0^{\infty}  dz \sin[x z +\frac{z^3}{3}].
\end{eqnarray}

Moreover, using integral representation of the modified Bessel function,
the r.h.s of the equation (\ref{intres2}) can be expressed as,
\begin{eqnarray}
\int_0^{\infty}  r dr \sin[\frac{3\rho}{2}(r+\frac{r^3}{3})] = \frac{ K_{2/3}[\rho] }{\sqrt{3}},
\end{eqnarray}
where $K_{2/3}[\rho]$ is the generalized Bessel function with $2/3$ weight \cite{abram}.
Now combining all the results we can finally write down the result of $s$ integral calculation,
 \begin{eqnarray}
\int_0^{\infty} s ds  e^{-i s\phi_0} =
 \frac{\pi}{m^4} {(\frac{3 \rho}{2 })}^{4/3}Gi'[{(\frac{3 \rho}{2 })}^{2/3}] -
i {(\frac{3 \rho}{2 m^2 })}^{2} \frac{ K_{2/3}[\rho] }{\sqrt{3}}.\nonumber \\
\end{eqnarray}

For our present analysis we are interested in the asymptotic region of the associated parameter $\rho $.
If we consider $\rho$ is very large ($\rho >>1$), the $s$ integral simplifies to,
\begin{eqnarray}
 \int_0^{\infty} s ds  e^{-i s\phi_0} = -\frac{1}{m^4} - i {(\frac{3 \rho}{2 m^2})}^2 \sqrt{\frac{\pi}{6 \rho}} e^{-\rho}.
\label{large}
\end{eqnarray}
Here we have used the following two asymptotic expansion \cite{abram},
\begin{eqnarray}
Gi'[x] \approx  - \frac{1}{\pi x^2}, \nonumber \\
K_{2/3}[x] \approx  \sqrt{\frac{\pi}{2 x}} e^{-x}.  \nonumber \\
\label{id5}
\end{eqnarray}
On the other hand, when $\rho$ takes small values ($\rho << 1$) the $s$ integral modifies as,
\begin{eqnarray}
 \int_0^{\infty} s ds  e^{-i s\phi_0} = \frac{\rho^{4/3}}{m^4} c_1,  ~~~~~
\Big(c_1 =  \Gamma[\frac{2}{3}] \Big(\frac{3}{2^{7/3}} -i \frac{3^{3/2}}{2^{7/3}} \Big) \Big).
\label{id6}
\end{eqnarray}
In deriving equation (\ref{id6}), we have used the following approximations \cite{abram},
\begin{eqnarray}
Gi'[x] \approx \frac{ 3^{-1/3} }{2 \pi}\Gamma[\frac{2}{3}], \nonumber \\
K_{2/3}[x] \approx 2^{-1/3}\Gamma[\frac{2}{3}] {x}^{-2/3}.
\label{id7}
\end{eqnarray}
Having the $s$ integral done, we aim to work out the $v$ integral within the restricted range of parameters.
For small values of $\lambda$ we combine the results mentioned in (\ref{large}) and (\ref{i1}),
\begin{eqnarray}
 I_1 &=& \frac{4 q^2 E^2}{15m^4} + \nonumber \\
&& \frac{3 i q^2 E^2}{2\sqrt{6} m^4 |{(\tilde{\mathcal{G}}_4)}_{00}|}
\sqrt{\frac{\pi \sqrt{|{(\tilde{\mathcal{G}}_4)}_{00}|}}{\lambda^3}}\int_0^1 dv \sqrt{1-v^2}~
\Big(\frac{5-6v^2+v^4}{{(1-v^2)}^2}\Big)~
e^{\frac{-4}{\lambda \sqrt{|{(\tilde{\mathcal{G}}_4)}_{00}|} (1-v^2) }}. \nonumber \\
\end{eqnarray}
Implementing the change of variable $x = \frac{1}{1-v^2}$ and applying the useful identity,
\begin{eqnarray}
 \int_{1}^{\infty} \frac{1}{\sqrt{x-1}}\frac{dx}{x^2}x^{\sigma}e^{-\delta x} \approx \sqrt{\frac{\pi}{\delta}}e^{-\delta}
\Big[1+ \mathcal{O}(\frac{1}{\delta}) \Big],
\end{eqnarray}
we get the final expression of $I_1$ for small $\lambda$,
\begin{eqnarray}
 I_1 &=& \Big(\frac{4 \omega_0^2}{15 m^2}\Big) +
 i\Big(  \frac{5 \pi}
{2\sqrt{6} \sqrt{{\tilde{\mathcal{G}}}_{00}}}
(\frac{\omega}{\omega_0}) \Big)e^{-\frac{4}{\lambda \sqrt{{\tilde{\mathcal{G}}}_{00}}}}~~~~(\omega_0 = \frac{qE}{m}).
\end{eqnarray}
Similarly the $I_2$ integral turns out to be,
\begin{eqnarray}
 I_2 &=& \Big(\frac{4 \omega_0^2}{45 m^2}\Big) +
 i\Big(  \frac{\pi}
{\sqrt{6} \sqrt{{\tilde{\mathcal{G}}}_{00}}}
(\frac{\omega}{\omega_0})\Big)e^{-\frac{4}{\lambda \sqrt{{\tilde{\mathcal{G}}}_{00}}}}.
\end{eqnarray}
For large $\lambda$, same type of computation yields,
\begin{eqnarray}
 I_1 &=& -\Big[\Big( \frac{2^{\frac{5}{3}} \sqrt{\pi} \Gamma[\frac{5}{3}]\Gamma[\frac{2}{3}]}{3^{\frac{4}{3}} \Gamma[\frac{13}{6}]} {(\frac{m \omega_0}{{\tilde{\mathcal{G}}}_{00} \omega^2})}^{\frac{2}{3}}\Big)
- i  \Big( \frac{2^{\frac{5}{3}} \sqrt{\pi} \Gamma[\frac{5}{3}]\Gamma[\frac{2}{3}]}{3^{\frac{5}{6}} \Gamma[\frac{13}{6}]}
{(\frac{m \omega_0}{{\tilde{\mathcal{G}}}_{00} \omega^2})}^{\frac{2}{3}} \Big) \Big], \nonumber \\
I_2 &=& -\Big[\Big( \frac{2^{\frac{5}{3}} \sqrt{\pi} \Gamma[\frac{2}{3}]^2}{7 \times 3^{\frac{4}{3}} \Gamma[\frac{7}{6}]}{(\frac{m \omega_0}{{\tilde{\mathcal{G}}}_{00} \omega^2})}^{\frac{2}{3}}\Big)
- i  \Big( \frac{2^{\frac{5}{3}} \sqrt{\pi} \Gamma[\frac{2}{3}]^2	}{7 \times 3^{\frac{5}{6}}
\Gamma[\frac{7}{6}]} {(\frac{m \omega_0}{{\tilde{\mathcal{G}}}_{00} \omega^2})}^{\frac{2}{3}}
\Big)\Big]. \nonumber \\
\end{eqnarray}
Combining (\ref{classical1}) and (\ref{covaction}) we construct the covariant form of
Maxwell action with the one-loop quantum correction in a four dimensional space time characterized by
$\tilde{\mathcal{G}}_4$. In the next section we study the gauge field dynamics governed by the covariant quantum corrected
action. In particular, with the boundary condition set at large $u$,
we solve the equation of motion for gauge field. Furthermore, by utilizing this solution, we follow the
 Kubo's prescription to compute a frequency dependent conductivity.

\section{Computation of frequency dependent conductivity} \label{four}
We consider the covariant form total effective action constructed in four dimensional curved space time,
\begin{eqnarray}
  S_{total} = \frac{1}{2} \int d^4 x \frac{1}{g_s^{eff}} \Big[ \dot{\tilde{\Xi}}^2 \Psi_1 - \tilde{\Xi}'^2 \Psi_2 \Big],
\end{eqnarray}
where $\Psi_1$ and $\Psi_2$ are the following,
\begin{eqnarray}
\Psi_1 (u)&=&  \sqrt{-Det\mathcal{\tilde{G}}_4} \frac{1}{u^3f(1-\frac{e^2}{fu^3})}
\Big \{ 1 - g_s^{eff} \mathcal{C}(I_1)\Big \}, \nonumber \\
\Psi_2(u) &=&  \sqrt{-Det\mathcal{\tilde{G}}_4}\frac{f }{u^3 (\frac{1}{u^3}+f {X_4'}^2)}
\Big \{ 1 - g_s^{eff} \mathcal{C} (I_2)\Big \}.
\end{eqnarray}
To write the total action consistently we have set $2 \pi l_s^2 = 1$. The relative sign between the classical and quantum part is
still to be defined. By comparing the standard
form $e^{iS_{\text{real}}}e^{-\Gamma} = e^{i(S_{\text{Real}} + i\Gamma)}$
 we conclude that the sign of the normalization constant is negative. For simplicity we set $\mathcal{C} = -1$.
 Assuming the space time structure of the gauge field
$\tilde{\Xi}(u, t) = \tilde{\Xi}(u) e^{-i \omega t}$ we get the equation of motion,
\begin{eqnarray}
\tilde{\Xi}''(u) \Psi_2(u) + \tilde{\Xi}'(u) \Psi_2'(u) + \omega^2 \Psi_1(u) \tilde{\Xi}(u) = 0.
\label{eomnew}
\end{eqnarray}
The solution of the equation of motion with appropriate boundary conditions contains both normalizable and non-normalizable modes.
The associated Green's function $G_R$ is defined as the ratio of normalizable to non-normalizable modes.
Using Kubo formula in linear response theory, the working formula for the conductivity can be constructed from the structure of $G_R$.
\begin{eqnarray}
 \sigma = \frac{G_R}{i \omega}.
 \label{sigma}
\end{eqnarray}
Before obtaining a solution of (\ref{eomnew}) we make a suitable coordinate transformation.
\begin{eqnarray}
 \mathcal{Y}^2 = 1-\frac{u}{u_0}.
\end{eqnarray}
In this coordinate system, the equation of motion takes the following form,
\begin{eqnarray}
 \Big[\frac{d^2\tilde{\Xi}}{d \mathcal{Y}^2} \frac{{(1-\mathcal{Y}^2)}^4}{4u_0^2\mathcal{Y}^2} - \frac{d \mathcal{Y}}{d\mathcal{Y}}
 \frac{(3\mathcal{Y}^2 +1){(1-\mathcal{Y}^2)}^3}{4u_0^2 \mathcal{Y}^3} \Big] \Psi_2
 + \Big[ \frac{d\tilde{\Xi}}{d \mathcal{Y}}  \frac{d\Psi_2}{d \mathcal{Y}} {\frac{{(1-\mathcal{Y}^2 )}^4}{4u_0^2 \mathcal{Y}^2}}\Big]
 \nonumber \\+ \omega^2 \tilde{\Xi} \Psi_1(u) =0.
\label{eomfull}
\end{eqnarray}

The range of $\mathcal{Y}$ is fixed as $[0,-1]$.
In the nine dimensional world volume theory of the $D8/\overline{D8}$, the above choice of $\mathcal{Y}$ coordinate
has a natural interpretation. The location where the $D8$ and $\overline{D8}$ meet is denoted by $\mathcal{Y} = 0$, whereas
the intersection points between the $D8$ and $\overline{D8}$ with $D4$ are specified as $\mathcal{Y} = \pm 1$. For
convenient nomenclature we refer $\mathcal{Y} = 1$ as the ``boundary'' and $\mathcal{Y} =-1$ as the `` horizon''.
For all subsequent analysis we set $u_{T} = 1$. The equation of motion for $\tilde{\Xi}(u) $ near the ``horizon''
becomes,
\begin{eqnarray}
 (1+ \mathcal{Y})\tilde{\Xi}''( \mathcal{Y}) -\frac{1}{2} \tilde{\Xi}'( \mathcal{Y}) +
\frac{2\omega^2}{u_0}\tilde{\Xi}(\mathcal{Y}) = 0.
\label{eom1}
\end{eqnarray}
While deriving the equation (\ref{eom1}) we have used the asymptotic form of $\Psi_1$ and $\Psi_2$.
\begin{eqnarray}
\Psi_1 &\approx& \frac{\sqrt{1-{\mathcal{Y}}^2}}{\sqrt{u_0}}\frac{1}{\hat{g}_s^{eff}}, \nonumber \\
\Psi_2 &\approx& \frac{u_0^{5/2}}{{(1-y^2)}^{5/2}}\frac{1}{{\hat{g}}_s^{eff}}.
 \label{psi1}
\end{eqnarray}

We aim to solve to the above equation of motion near ``horizon'' in leading order of $ \mathcal{Y}$. Considering the newly
defined argument $\mathcal{Z}$, satisfying
\begin{eqnarray}
 \Psi_2 \frac{d}{d\mathcal{Y}} = \frac{d}{d\mathcal{Z}},
\end{eqnarray}
we re-write the equation (\ref{eom1}) as follows
\begin{eqnarray}
 \frac{d^2\tilde{\Xi}}{d^2\mathcal{Z}}+\omega^2 \Psi_1\Psi_2 \tilde{\Xi} = 0.
\end{eqnarray}
Choosing a suitable ansatz leads to the following set of equations,
\begin{eqnarray}
\tilde{\Xi} &=& e^{-S(\mathcal{Z})}, \nonumber \\
\tilde{\Xi}'' &=& -S''(\mathcal{Z}) e^{-S(\mathcal{Z})}+{S'(\mathcal{Z})}^2 e^{-S(\mathcal{Z})}.
\end{eqnarray}
Ignoring $S''(\mathcal{Z})$ for the leading order solution we get,
\begin{eqnarray}
S = \int^\mathcal{Z} \pm i\omega \sqrt{\Psi_1\Psi_2} d\mathcal{Z}'.
\end{eqnarray}

The form of $\Psi_1$ and $\Psi_2$ at $\mathcal{Y} = -1$ is easy to derive from (\ref{psi1}).
Therefore, by solving the equation (\ref{eom1}), we get the leading term in $\tilde{\Xi}$,
\begin{eqnarray}
 \tilde{\Xi} = e^{\pm i \frac{2\sqrt{2}\omega}{\sqrt{u_0}} \sqrt{1+\mathcal{Y}}}.
\end{eqnarray}
For computation of the conductivity usually one has to employ the ingoing boundary condition at some location in the
space time where
the flavor brane touches the real horizon of black hole background.
In our analysis, neither the flavor branes touch the black hole
horizon nor any induced horizon gets developed in the  world volume. Similar kind of situation has been discussed in \cite{KSSS},
where the background holographically corresponds to a confining phase of a strongly coupled system at finite temperature.
Since they have studied a system with real Lagrangian, they make a choice of
a complex boundary condition at $\mathcal{Y} = -1$ to get a
finite real part of the conductivity. However, in our
case the Lagrangian is complex. So the most general choice is the standing wave ansatz, i.e, the real boundary condition,
\begin{eqnarray}
\tilde{\Xi} &=& c_1 e^{ i \frac{2\sqrt{2}\omega}{\sqrt{u_0}} \sqrt{1+\mathcal{Y}}} +
c_1^* e^{ -i \frac{2\sqrt{2}\omega}{\sqrt{u_0}} \sqrt{1+\mathcal{Y}}}, \nonumber \\
&=& \cos[\frac{2\sqrt{2}\omega}{\sqrt{u_0}} \sqrt{1+\mathcal{Y}}+\phi],
\end{eqnarray}

where $c_1$ is an arbitrary constant and $\phi$ is the phase.
We make a choice at $\mathcal{Y}=-1+\epsilon$, $\phi= -\frac{2\sqrt{2}\omega}{\sqrt{u_0}} \sqrt{\epsilon} $.
As a result of this choice, we can define the boundary conditions,
\begin{equation}
 \tilde{\Xi}(\mathcal{Y} = -1) \sim 1, ~~~~~~\tilde{\Xi}' (\mathcal{Y} = -1) \sim 0.
\label{bndcond}
\end{equation}
At the ``boundary'', $\mathcal{Y}=+1$ the equation of motion simplifies as,
\begin{eqnarray}
 (1-\mathcal{Y})\tilde{\Xi}'' +\frac{1}{2} \tilde{\Xi}' + \frac{2\omega^2}{u_0}\tilde{\Xi}= 0.
\end{eqnarray}
The series solution for $\tilde{\Xi}(\mathcal{Y})$  near $\mathcal{Y}=+1$ reads as,
\begin{eqnarray}
 \tilde{\Xi}(y) &=& M \Big[1+M_1 (1-y) + M_2 {(1-y)}^2 + .....\Big],  \nonumber \\
 && ~~~~~~~~~~~~~~~                            + N{(1-y)}^{3/2} \Big[1+N_1 (1-y) + N_2 {(1-y)}^2 + .....\Big],
\end{eqnarray}
where $M$ and $N$ are the parameters to be determined by boundary conditions and $M_i$ and $N_i$ depend on the
parameters of the theory.
The Green's function of our interest is given by,
\begin{eqnarray}
 G_{R} \sim \frac{N}{M} = \frac{4}{3}\frac{\sqrt{1-\mathcal{Y}}}{\tilde{\Xi}(\mathcal{Y})} \frac{d^2\tilde{\Xi}}{d\mathcal{Y}^2}.
\label{Greenfn}
\end{eqnarray}

\begin{figure}[h]
 \centering
 \mbox{\subfigure[]{\includegraphics[width=7.0 cm]{smallfig1.eps}}
 \quad
\subfigure[]{\includegraphics[width=7.0 cm]{smallfig2.eps} }

}
 \caption{Fig (a) and (b) depicts the real part of the conductivity for the set of parametric values
($E = \frac{1}{10^2}$, $m = 5$) and ($E = \frac{1}{10^2}$, $m = 10$). Here we have chosen $u_0 = 10 $.}
 \label{condfig11}
 \end{figure}
 \begin{figure}[h]
 \centering
 \mbox{
\subfigure[]{\includegraphics[width=7.0 cm]{smallfig3.eps} }
\quad
\subfigure[]{\includegraphics[width=7.0 cm]{smallfig4.eps} }
}
 \caption{Fig (a) and (b) shows the real part of the
conductivity with the choices of the parameters are
 ($E = \frac{1}{50}$, $m = 5$) and ($E = \frac{1}{50}$, $m = 10$) respectively. Here we have chosen $u_0 = 10 $.}
 \label{condfig22}
 \end{figure}

 \begin{figure}[h]
 \centering
 \mbox{\subfigure[]{\includegraphics[width=7.2 cm]{largefig1.eps}}
 \quad
\subfigure[]{\includegraphics[width=7.2 cm]{largefig2.eps} }}
 \caption{ In this figure we have plotted the real part of the $\sigma$ with respect to $\omega$ for
 the set of parametric values
 ($E = \frac{1}{30^3}$, $m = \frac{1}{100}$) and ($E = \frac{1}{2\times 30^3}$, $m = \frac{1}{100}$). Here we have chosen $u_0 = 1000$.}
 \label{condfig33}
 \end{figure}

  \begin{figure}[h]
 \centering
 \mbox{\subfigure[]{\includegraphics[width=4.6 cm]{compare1.eps}}
 \quad
\subfigure[]{\includegraphics[width=4.6 cm]{compare2.eps} }
\quad
\subfigure[]{\includegraphics[width=4.6 cm]{compare3.eps} }

}
 \caption{Fig (a), (b) and (c) depict the variation of the separation between two consecutive peaks in Re $\sigma$ vs $\omega$ plot
 for three different
 values of $u_0 = 10, 100, 500$. The choice of others parameters are fixed as ($E = \frac{1}{2\times 30^3}$, $m = \frac{1}{100}$)}
 \label{condfig44}
 \end{figure}

Finally the conductivity is calculated by inserting the form of $G_R$ in (\ref{sigma}). Here we actually solve the equation (\ref{eomfull})
subject to the boundary conditions (\ref{bndcond}) using numerical methods. Then we apply the full solution together with (\ref{sigma}) and
(\ref{Greenfn}) to compute the conductivity at the `` boundary'' $\mathcal{Y} = 1$. Finally, we plot the real part of the conductivity with respect to
the frequency for both small and large $\lambda$. For example, figure (\ref{condfig11}) and  (\ref{condfig22})
show the variation of the real part of $\sigma$ with respect to frequency for $\lambda < 1$. We
also show the same for  $\lambda > 1$ in figure  (\ref{condfig33}).
\pagebreak
From both cases it is evident that if we increase the mass, the conductivity is less.
On the other hand conductivity enhances with the external electric field. For large and small
$\lambda$, real part of the conductivity seems to diverge periodically with respect to $\omega$. The
periodicity of this divergence almost remains constant as we vary the parameters $m$ and $E$.
For $\lambda < 1$ we observe that the conductivity takes negative value with respect to the  higher values of frequency.
For $\lambda > 1$, the region of negative conductivity lies within the lower range of $\omega$.
For higher range of $\omega$ it is positive and always periodically divergent. In fig (\ref{condfig44})
we have plotted the conductivity for three different values of $u_0 = 10, 100, 500$ keeping the electric field
$E = \frac{1}{2\times 30^3}$ and  $m = \frac{1}{100}$ fixed. We observe in this plot that for lower values of $u_0 = 10$ the real part
of the $\sigma$ takes negative values. As we increase the $u_0 = 100, 500$ the conductivity is always positive. Most importantly, the
frequency of the peaks in conductivity plots scales as $\sqrt{u_0}$.
These peaks may arises from the poles of the Green's function and the corresponding frequency modes are well known as normal/quasi-normal modes.
In the confined phase of Sakai-Sugimoto model, the normal modes determines the mass of the meson spectrum and the mass parameter turns out to
be proportional to the Kaluza-Klein mass ($m_{KK}$) of the theory.
Since $m_{KK}$ scales as the square root of $u_{KK}$, the period of  normal modes also scales as $\sqrt{u_{KK}}$.
In our case, we have set the $u_{KK} =1$ and in the deconfined phase the role of $u_{KK}$
is played by the radius of horizon $u_{T}$ (the $u-x_4$ subspace is a topologically cylinder). Therefore the only relevant parameter
to set the mass scale is $u_0$. As we already observe that the periodicity
of the frequencies where the conductivity (evaluated numerically) seems to diverge  scales as $\sqrt{u_0}$. So it is tempting to conclude
that these apparent numerical divergences are in fact  poles appearing in the Greens's function and actually characterize the quasinormal modes.

\pagebreak

\section{Conclusion} \label{five}

In this paper we have discussed the effect of pair production in modifying the conductivity
in strong coupling situations. The strong coupling theory is  described holographically by a
system of flavor and color branes. The flavor branes provide flavor quantum numbers to particles.
The one loop Schwinger effect modifies the effective action for a photon on the flavor brane. Since the coupling constant $g^2_{YM}=g_s$ is small, this one loop calculation is reliable. The photon is dual to a conserved current in the boundary theory. The current current correlator in the boundary is modified. This modifies the conductivity of the boundary theory. The interesting point is that because the Schwinger effect introduces an imaginary part to the effective action, the modified conductivity in the boundary acquires a real part. Thus
an insulator starts to have a small real conductivity in the presence of an electric field.
What is doubly interesting is that the differential conductivity for some range of parameters can be
{\em negative}. This effect is known in condensed matter contexts in semiconductor diodes such as tunnel diodes and Gunn diodes although the mechanism of negative differential resistance is specific to the device. Here we have a strong
coupling version of this. This is similar to the effect discussed in \cite{Nakamura-Ooguri,Nakamura1,Nakamura2}.
The main difference is that in these papers  the effect was already there at the classical level on the flavor
brane because of the presence of an open string metric horizon. In our case there is no such horizon and shows
up only at one loop.

It would be interesting to identify experiments analogous to those suggested in \cite{ACG} where the Schwinger effect would be observable.

\section*{Acknowledgements}
The authors would like to acknowledge Ganapathy Baskaran, S. Kalyana Rama, Nemani V. Suryanarayana,
Sudipta Mukherji, Amitav Virmani and Swarnendu Sarkar for various fruitful discussions.
S.C would like to thank Sudipto Paul Chowdhury and Sunanda Patra for useful discussion.

redpajama_set_name: RedPajamaArXiv


Do not give prochlorperazine to a child younger than 2 years old or weighing less than 20 pounds.
If you need surgery or a medical procedure, tell the doctor you currently use prochlorperazine. You may need to stop for a short time.
Avoid driving or operating machinery until you know how prochlorperazine will affect you. Dizziness or drowsiness can cause falls, accidents, or severe injuries.


The Respirators (also Gas Masks) are special gear that Lara can find in Lara Croft Tomb Raider: The Angel of Darkness. Inside the Louvre is a case containing three Respirators.
The case can first be seen in the Louvre Galleries level, and can not be opened until the Galleries Under Siege level. However, there is a trick that enables you to get them earlier. Walk up to the case and crouch down. While Lara is about to crouch the hand symbol appears, press crouch and action and Lara will grab one of the masks. You can repeat this until all of the masks have been picked.
The Respirators can be used underwater like the Aqua - lung. When using the bug in the Louvre Galleries, they can be used in Neptune's Hall and also later in the level The Vault of Trophies, giving Lara a big advantage.
Don't save underwater: Lara can breathe but she's not invincible, and the Breath Bar will still eventually run out despite of using the Respirators/Aqua - lung.
When you get back to the Galleries Under Siege all respirators will be back in the case and can be picked up again, to be used to prevent Lara from taking damage from poisonous gas.
Protects against dangerous fumes during restoration processes.
An attachment to the Extreme Depth Suit found in the Deepsea Dive level of Tomb Raider Chronicles, which allows Lara to breath underwater indefinitely, or at least until the suit is damaged.
Another breathing apparatus in The Angel of Darkness. This one has been designed to work underwater and is found in the level The Vault of Trophies.
A similar apparatus found in the region Flooded Archives of Rise of the Tomb Raider, during the level Dark Waters.
This page was last modified on 17 November 2016, at 18:27.


Giants of Colossus Progressive Rock Recording Artists on the Naked Hoof® label.
NYCSmoke more genuine NYC rock 'n roll.
Bruce Colfin Entertainment attorney. A decent guy who won't rip you off.
Jeffrey Jacobson Entertainment attorney. Another decent guy who won't rip you off.
Adobe the makers of Photoshop.
Naked Hoof and the Naked Hoof logo are registered trademarks of Bill Anderson.
All content on this domain copyright ©2015 Bill & Bev Anderson & Naked Hoof.


Here you can find many resources for learning how to best utilize our system. The documentation is designed to allow you to learn how to do specific things with the system as opposed to being an exhaustive resource for all functionality. If you're looking for something specific, we have a handy search bar for you along the top!
Most users, especially those savvy with Excel, also interact with the Reporting Library on a frequent basis. We also have several categories of Reports for you to choose from. Below is a handy breakdown of the categories.


Arizonas . tarahot4. LindsayMilly. VladaMoore.
SuperMollyLylaDreamFamefameLylaDream .NathanSexySlimtarahot4KassandraHot26SaidLoveMerry .myssika2121linasmithSarrahHotHotAncientEve .3crazyhorny20CarolineLovingAnnieRedRossie .SandyFayXIzzie010SweetyMinaBarneyWaters .SecrettEthiz2MarissaMellowCELINExNIGHT .cherrybombinayMiaSorenteJessicaRavanHannahCY .LatinNoirCplSexyAaronkSizzlingEYAMRaimondaCan3 .MiaDousonCameronSmithMiemadieEvebel .cherrybombinayAlessiaBaileyVladaMooreCELINExNIGHT .AlessiaBaileySarrahHotMakedaQueenCameronSmith .
TasayAgnesQuinnEivaThornecouplebigtits0 .GlamBunniesMayaXHotEastDelightsHotAncientEve .SweetyMinaRaimondaCan3Famefamecouplebigtits0 .SweetyMinaSimonaDancGirlCarolineLovingAgnesQuinn .naughtywondersInsidiousCOCKSizzlingEYAMEivaThorne .RolandMusclesSarrahHotTasayRolandMuscles .MeganGraceMeganGraceAllyJayCameronSmith .YasminAsiaEmilyPresleyGlamBunniesMeganGrace .tarahot4CELINExNIGHTnaughtywondersKristynLube .EmilyPresleyLindsayMillyBarneyWatersWhitneyWonder .GlamBunniesScarletFireRoseYourLovelyJessRossie .


text:
Events
January 1 – Arnold von Bruck retires from his position as Kapellmeister at the Viennese court.
May - Cipriano de Rore appointed maestro do cappella at the court in Ferrara, a post he held until 1559.
Jacquet de Berchem appointed maestro di cappella at Verona Cathedral

Publications
Giulio Abondante - , the first of three extant books of lute music published in Venice by Antonio Gardano
Paolo Aretino – Pie ac devotissime Lamentationes Hyeremie prophete tum etiam Passiones Hiesu Christi Dominice Palmarum ac Veneris Sancti (Venice: Angelo Gardano), a collection of litanies
Jacquet de Berchem – First book of madrigals for five voices (Venice: Antonio Gardano)
Simon Boyleau – Madrigals for four voices
Antoine de Mornable
, book 1, for four voices (Paris: Pierre Attaingnant)
17 Psalms for four voices (Paris: Pierre Attaingnant)
Alonso Mudarra - 'Three Books of Music for vihuela in tablature' (Seville: Juan de Leon)
Caspar Othmayr –  for five voices (Nuremberg: Johann vom Berg & Ulrich Neuber)
Girolamo Parabosco – Madrigali a cinque voci (Venice: Antonio Gardano)

Classical music
Giovan Tomaso di Maio – Canzone villanesche a 3, book 1

Births
date unknown –
September 3 – Isabella Bendidio, Italian noblewoman and singer (died 1610)
October 5 – Cyriakus Schneegass, German hymnwriter (d. 1597)
date unknown
 Luca Bati, Italian composer (died 1608)
 Joachim a Burck, German hymn writer, composer, organist and Kantor (died 1610)

Deaths
 Fridolin Sicher (56), organist and composer

References

Music
16th century in music
Music by year

redpajama_set_name: RedPajamaWikipedia


A surprise strong showing by a new anti-corruption party in India has helped to topple the ruling Congress party in Delhi assembly elections.
The leader of the Common Man's Party, Arvind Kejriwal, has defeated Delhi's long-serving Congress chief minister Sheila Dikshit and taken her seat.
In Delhi, party supporters danced and waved brooms - the symbol of their party - in the air.
The Congress party has also lost control of Delhi's 70-seat assembly.
The party of the Nehru-Gandhi dynasty that has ruled India for most of its existence as an independent nation has been humiliated in these polls, in what is being seen as a wave of rebellion against its handling of the economy - and corruption, says the BBC's Andrew North in Delhi.
Mr Kejriwal defeated the three-time chief minister of Delhi in her own constituency, which she had held for 15 years, and his party came close to winning control of the city.
His party now controls nearly 40% of the Delhi assembly seats.
Addressing supporters after his victory, Mr Kejriwal said: "I'm fully confident that finally the country will win, people will win, democracy will come, and India will win."
The clear winner has been the opposition BJP - giving a major boost for its controversial candidate for prime minister, Narendra Modi, our correspondent says.
Early tallies indicate that the Hindu nationalist BJP is leading in the states of Rajasthan, Madhya Pradesh as well as in Delhi, while it is in a close fight with Congress in the central Indian state of Chhatisgarh.
The vote is seen as a key test for the two main parties, the governing Congress and the opposition BJP, ahead of next year's general elections.
But these results underline the scale of the challenge the Congress party faces in hanging on to power, our correspondent adds.
The Aam Admi (Common Man's) Party was born out of a strong anti-corruption movement that swept India two years ago.
I am proud to have campaigned for AAP. Be the change.


text:
Home / Clockwork Pi / News / Reviews / The Retro-Portable Clockwork Pi The Raspberry Pi Compute Module 4 SOM Adapter is Now Available for DevTerm.
The Retro-Portable Clockwork Pi The Raspberry Pi Compute Module 4 SOM Adapter is Now Available for DevTerm.
by in Clockwork Pi, News, Reviews
The Raspberry Pi Compute Module 4 and an in-house RISC-V architecture are among the new SOM family possibilities for the DevTerm.
Clockwork Pi has announced a major addition to its retro-style portable PC, the DevTerm: a new system-on-module (SOM) adaptor that accommodates a Raspberry Pi Compute Module 4.
The Clockwork Pi DevTerm, announced in 2020 and released last year, is a plastic-encased small portable computer inspired by the Kyocera Kyotronic 85 and its more well-known spin-off, the TRS-80 Model 11. The kit-form device, which features an ultra-wide display and a compact QWERTY keyboard with a tiny trackball, is powered by a carrier board that houses one of three systems-on-modules: the A-06 range with a Rockchip RK3399 six-core processor, the A-04 with a quad-core chip, or a Raspberry Pi Compute Module 3.
The R-01, the company's first post-launch SOM design, was introduced earlier this year, based around Allwinner's D1 system-on-chip, which hosts a single since-opened 64-bit RISC-V processor. Despite being classified as somewhat experimental, owing mostly to continuing software development work, the initial reaction to the gadget has been overwhelmingly favorable.
Clockwork Pi has now announced its second alternative SOM — or, more precisely, an adapter that allows the powerful Raspberry Pi Compute Module 4, with its twin high-density connectors on the underside instead of the Compute Module 3's SODIMM-style edge connector, to slot directly into the DevTerm carrier board.
Once installed, the CM4 should be able to run Raspberry Pi OS directly on the DevTerm — though, at the time of writing, Clockwork Pi hadn't confirmed whether it intended to port its software for devices such as the on-board thermal printer or if it would instead offer its own customized operating system.
There are certain limitations to its use as well. The first is that utilizing the Raspberry Pi Compute Module 4 disables the DevTerm's internal Wi-Fi, even if you buy one without an onboard radio. The second is that selecting a CM4 with onboard eMMC storage removes the DevTerm's externally accessible microSD slot — but with the benefit of speedier storage access.
The adapter is available now for $19 on its own or $238 as part of a complete DevTerm Kit on the Clockwork Pi shop — but you'll need to supply your own Raspberry Pi Compute Module 4. However, you will receive the adapter, an add-on Wi-Fi antenna, and an "ultra-thin heat sink set" to keep temperatures under control.
Tags # Clockwork Pi # News
Tags: Clockwork Pi, News, Reviews

redpajama_set_name: RedPajamaCommonCrawl


text:
class MyContextManager(object):
	def __init__(self, value):
		self.value = value
	def __enter__(self):
		if self.value == "raise_on_enter":
			raise ValueError(repr(self.value))
		print "__enter__", self.value
		return self.value
	def __exit__(self, typ, value, traceback):
		if self.value == "raise_on_exit":
			raise ValueError(repr(self.value))
		print "__exit__ type=%r, value=%r, traceback=%r" % (typ, value, traceback)
		#return True
	def njakz():
		pass

with MyContextManager("ok") as njak:
	print 'inside', njak

# with MyContextManager("raise_on_enter") as njak:
# 	print 'inside', njak

# with MyContextManager("raise_on_exit") as njak:
# 	print 'inside', njak

# with MyContextManager("raise_from_inside") as njak:
# 	raise ValueError(njak)

# Be careful with @contextmanager, yield must be in try-finally
from contextlib import contextmanager

###############################################################################
@contextmanager
def yourContextManager(value):
	# save
	pass
	try:
		# yield inner
		pass
	finally:
		# restore
		pass

for ii in xrange(10):
	print ii

assert ii == 9, "lol, where is your scope python"

###############################################################################
#Nested functions
def njak(a, b):
	def zrak(a, b):
		return a + b
	return zrak(a, b) * 2

exec 'print "njak", njak(3, 4)'

###############################################################################
my_global = 33

def inc_global():
	global my_global
	my_global += 1

inc_global()
print my_global

###############################################################################
class Jan:
	haha = 37   # class global variables should be either read-only
	tricks = [] # or lists/dicts
	def __init__(self, a, b):
		self.a = a
		self.b = b
	def janMethod(self, a, b):
		return a + b
	def febMethod(self):
		return "february" + str(self.a) + str(self.b)

jan1 = Jan(3, 4)
jan2 = Jan(5, 6)

j1f = jan1.febMethod
j2f = jan2.febMethod

print j1f(), j2f()

jan1.haha += 1 # two instances of haha in the += operator do NOT point to the same object!!!
print jan1.haha, Jan.haha, jan2.haha

jan1.tricks.append('aaa')
jan2.tricks.append('bbb')
print jan1.tricks
print jan1.__class__

class Feb(Jan):
	def __init__(self, a):
		Jan.__init__(self, a, 77)

feb1 = Feb(33)

print feb1.febMethod()

###############################################################################
class MarError(BaseException):
	pass
	# def __init__(self, a, b):
	# 	self.a = a
	# 	self.b = b
	# 	self.args = (a, b)
	# def __str__(self):
	# 	return "muhaha" + self.a + self.b

try:
	raise MarError(45, 67)
except MarError as instance:
	print instance.args
	print instance

# do not override exception __init__ without args and __str__ override

###############################################################################
def squares():
	i = 1
	while True:
		yield i * i
		i += 1

###############################################################################
from functools import wraps

def square_result(func):
	@wraps(func)
	def inner(*args, **kwargs):
		result = func(*args, **kwargs)
		return result * result
	return inner

def add2(a, b):
	""" my add2 function"""
	return a + b

decorated = square_result(add2)
print decorated(3, 4)
print decorated.__doc__

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Home / Our Conferences / Sulaymaniyah Conference 2022
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STARTING OVER FROM SOLIDARITY
Final Declaration of ICSSI 2022 Conference
Sulaymaniyah, 11th-16th March 2022
ICSSI held its 11th international conference in Sulaymaniyah from 11th to 13th March 2022. Civil society activists from all over Iraq and from abroad gathered in Iraqi Kurdistan for a three-day conference to discuss the current situation within Iraqi civil society. Three years have passed since our last gathering in Baghdad, when ICSSI's 10th anniversary was celebrated. Since 2019, events, both in Iraq and internationally, prevented us from meeting regularly. This year's conference therefore represented a unique occasion to reconnect and strengthen our solidarity.
Solidarity, we believe, is the only answer to the appalling violence currently raging in Ukraine. We stand in solidarity with all the people who bravely struggle for peace within a context of increasing polarization, be they activists, journalists or human rights defenders in both Ukraine and Russia.
The last couple of years have been significant for Iraqi society and history. From the widespread participation in the October uprisings to the social and economic effects of the Covid-19 pandemic, through the limitations imposed to freedom of expression and freedom of the press all over the country and the brutal violence used against demonstrators and human rights defenders, it is undeniable that the situation in Iraq presents many challenges. However, today Iraqi civil society sees — and is seizing — many opportunities.
Representatives of 27 civil society organizations – both Iraqi and international – took part in the conference, ensuring a diverse range of perspectives on a set of topics. Members of local forums, as well as the Iraqi and Kurdistan social forum, ensured a focus on those issues which are most relevant at a local and grassroots level.
The agenda of the conference mirrored the work done over the last couple of years and came through consultation with the Iraqi social forum. The first day of conference was entirely devoted to the Kurdistan, Iraqi and local social forums, highlighting civil society's methods of working collectively. During the second and third days, plenary sessions and working groups focused on 4 general topics:
civil society and democracy – freedom of expression and freedom of the press, the shrinking spaces for civil society, post-election scenarios and women's political participation;
nonviolence, peacebuilding and protection of human rights defenders – prevention of violent extremism and the domestic violence law, the living conditions of human rights defenders in Iraq;
education and social, economic and cultural rights – the right to education, workers' rights and the experience of social entrepreneurship – environment and cultural heritage – protection of Iraqi cultural heritage, climate change and water management.
The days in Sulaymaniyah were days of intense work and animated discussion. The conference enabled us all to reflect more deeply on the challenges faced by Iraqi civil society — as well as those facing international civil society — and revealed the urgent need to strengthen the solidarity among all of us who are working at the local level to bring about more justice and peace. This was possible thanks to the active participation of all the attendees to the different sessions, but also thanks to a number of people who supported the conference organizing. We would like to thank all those who participated with us in this important event, all volunteers for their valuable support, the interpreters for their patience and commitment, CCFD – Terre Solidaire for their constant support, the organizations and individuals who donated time and energy to make this event happen, and finally, the ICSSI team for their tireless efforts devoted to making this conference a reality.
The following are some key recommendations generated by the working groups during the 2nd and 3rd days of the conference, the results of various campaigns' coordination and meetings of the General Assembly.
(2nd and 3rd day) Iraqi civil society Recommendations
CIVIL SOCIETY AND DEMOCRACY
Freedom of Expression and Freedom of the Press
Increase the attention to and work on the issue of cybersecurity for Iraqi activists, journalists and civil society organizations.
Enhance coordination and share knowledge of Iraqi CS with international experts on cases of violations of freedom of expression and the press in Iraq and on existing best practices and examples of successful advocacy.
Create links between Iraqi and international independent journalists.
Update and fill the gaps in the existing, obsolete, Iraqi law framework (3025) on freedom of expression and the press, the Iraqi penalty law (1969) on the protection of journalists, publication of crimes and the project of the media and communications authority.
Amplify the relevance of and give special protection to women's voices.
Work on making new journalists believe in an independent press and freedom of expression.
Observe and follow up on court trials against Iraqi activists and journalists.
Post-elections and the future of October Uprisings
Recognize the significance of the demonstrations held between 2003 and 2019, their role in calling for a common Iraqi identity and against divisive rhetoric.
Recognize that the protest's requests were not satisfied by any subsequent government, all of which were created to act on narrow partisan interests distant from those of the Iraqi people.
Reflect on the fact that the call for early elections has been co-opted by the government.
Realize key mistakes such as the attempt to separate advocacy from politics which has weakened the the possibility of effective civic action rising from Tishreen.
Shrinking spaces for Civil Society
Because work spaces for Iraqi civil society are rapidly shrinking, there is now a real threat to basic freedoms and sustainable democracy in Iraq. In response, ICSSI will establish a permanent working group to address the following:
Reviewing the legal framework for civil society organizations in Iraq and current administrative procedures constituting an obstacle to their freedom and security.
Collaborating with other NGOs to ensure that Iraq is fulfilling International Standards on issues pertaining to civil society.
Promote a robust and active definition of women's political participation; it is insufficient for women merely to be a "presence" (quotas), but they must be an effective part of the decision-making process in every aspect of social and political life.
Work on the Iraqi National Action Plan on women and expand existing resources for enhancing women's participation.
Share knowledge and explore innovative and contemporary methods for women's involvement, recognizing the importance of working on the social and cultural dimensions for promoting their political empowerment.
Include the issue of women's role and participation in society within education programs.
Promote a new conception of feminism as inclusive of men's participation and not against cultural traditions and dignity, countering the stigmatization of the feminist movement in Iraq.
NONVIOLENCE, PEACEBUILDING, AND HUMAN RIGHTS DEFENDERS
Prevention of Violent Extremism (PVE)
Restore Iraqi and KRI platforms for PVE's coordination for pursuing a common strategy and deepening knowledge of available tools and research in the sector.
Create contacts between Iraqi and International Civil Society experts and organizations working on PVE, enhance Iraqi civil society work on PVE by sharing experiences and lessons learned internationally.
Establish consistent and thorough follow ups after training activities on PVE to ensure and verify their effective and long-term results.
Engage with Iraqi youth who left school; develop innovative ways to reach those in a condition of social exclusion, encouraging them to become actively involved and trained in peacebuilding and issues surrounding human rights and nonviolence.
Recognize the importance of political advocacy for people's needs and social inclusion for achieving effective PVE.
Provide support to the Iraqi activists who have been targeted and abused because they participated in protests; work for human rights and political change as a way to prevent their radicalization.
Counter political manipulation of PVE, alerting international and Iraqi institutions on the risks of its misuse in human rights activist's criminalization and persecution.
Countering Domestic Violence
Enhance the ongoing campaign to promote the Law Against Domestic Violence in Iraq by preparing and disseminating a clear and easily understandable draft of the law; tackle the issue of opposition against women shelters; strengthen networks and mobilize people so that it will be passed in the Iraqi Parliament.
Invest in the potential of women's activists which was made clear during October's Uprisings.
Innovate existing methods for advocating for women's rights.
Establish stable collaboration with the High Commission for Human Rights in Iraq (HC) thus expanding their knowledge and understanding of the importance of the Human Rights Defenders issue, especially in Iraq.
Invite European and UN bodies (including the Special Rapporteur on Human Rights Defenders) to Iraq; call on the Iraqi Government to recognize the role and conditions of Iraqi Human Rights Defender's; set up and implement a legal framework for their protection.
Enhance and coordinate monitoring efforts on the cases of violation and abuse against Iraqi Human Rights Defenders in each governorate of Iraq.
Support the Protect Iraqi Human Rights Defenders NOW! Campaign and its connections at the local and international level.
EDUCATION AND ECONOMIC, SOCIAL AND CULTURAL RIGHTS
Worker's rights and Economic Policies
Prevent the privatization of essential services; promote and defend the de-privatization of basic services, such as education, housing, and health.
Support the goals of workers' syndicates' and their capacity-building.
Support the requests of workers' syndicates' by ensuring the diversity of their work and the freedom to create syndicates in all sectors, whether public, private or common.
Promote the enforcement of Iraqi laws on labor rights, social security, anti-corruption, and transparency.
Support Iraqi Social Forum Education Path; working on alternative budgeting to develop and promote new policies for the education sector in Iraq.
Use litigation as a tool for fighting corrupt systems impacting the enforcement of the right to education.
Lobby to reform the regulation 5/2013 into law for private education.
Involve teachers and students in the decision-making process relating to education in Iraq.
Promote an economy which cultivates and supports social solidarity and social enterprise in order to create and maintain economic activity within civil society.
Prepare and disseminate a model of how social enterprises work; ensure that this knowledge is readily available to Iraqi civil society and youth; verify the existing conditions for the establishment of new social enterprises/businesses within the Iraqi context.
Identify and share sources of funds for social enterprises in Iraq and internationally (e.g., grant opportunities).
Create opportunities for exchanges of practices of international and Iraqi social enterprises, especially those currently working in Iraq.
Seek opportunities to establish spaces where business ideas can be considered and created; support systems for the establishment of new social enterprises.
Encourage start-ups and micro-businesses which might then become thriving social enterprises that contribute to the well-being of local communities and have a broader positive impact on society.
Call on authorities to improving and adapt the legal framework for social enterprises.
ENVIRONMENT AND CULTURAL HERITAGE
Reflect critically on current production and consumption models; explore available alternatives for systemic transformation.
Find and secure support from international actors to pursue violations against environmental and human rights by oil companies, which is urgent given the high risk of confronting in-country actors.
Advocate for a stronger legal framework for oil companies and for increasing the use of clean and renewable energy sources.
Engage students and teachers in creating learning opportunities about the impact of climate change and the need for alternative systems.
Ensure the follow-up on environment-related and relevant government policies and reports.
Amplify the voices of Iraqis affected and displaced by climate change on their local communities.
Analyze Iraq's Annual Budget, study its environmental impact and advocate for allocating money to combat climate change and develop climate adaptation strategies.
Engage and empower the Iraqi Ministry of Environment to follow up on recommendations and environmental campaigns objectives from Iraqi civil society.
Environmental protection and water management
Promote and increase the activity of the Iraqi Social Forum Environment Path, setting its priorities.
Enhance networking with new voluntary teams and environmental initiatives occurring in Iraq.
Develop new environmental teams by providing specialized training.
Create more links with International environmental movements.
Promote internal environmental policies to be applied by Iraqi and international civil society organizations and groups operating in Iraq.
Hold the international community responsible for the environmental impacts of companies' activity in Iraq, with a special focus on the challenges posed by oil and water infrastructure (dams) companies.
Promote Iraqi civil society participation in all forums and opportunities for networking with environmental movements (including the Norwegian Social Forum in October 2022).
Keep the focus on Sustainable Development Goals while developing civil society action for the environment.
Build the Iraqi civil society capacity to collect documentation, analyze data and impacts on the environment in a professional way.
Promote activity by Iraqi civil society in, and knowledge of, the Business and Human Rights sector to enhance their work for companies' accountability.
Advocate for the protection of cultural and natural heritage in Iraq, particularly using art in all its forms.
Pressure all sources of financial support to invest in the protection of Iraq's natural and cultural heritage, giving proper financial support to those colleges and institutions specialized in the sector.
Promote the standards of eco-responsible tourism.
(4th day) Campaigns' coordination
On the 15th of March, a working group on women's rights and the three main ICSSI campaigns: Save the Tigris, End Cross-Border Bombings and Protect Iraqi Human Rights Defenders NOW! collaborated to achieve the following:
Establishment of internal strategic meetings to enhancing their networking and strategy-building thanks to focused face-by-face dialogue.
Identification of specific mutual goals based on cross-campaign coordination, for instance, End Cross Border Bombings and Save the Tigris Campaigns stated their mutual interest in working together on the environmental impact of the ongoing bombings in northern Iraqi Kurdistan, while the members of Protect Iraqi Human Rights Defenders NOW Campaign restated their shared engagement in protecting and supporting Women Human Rights Defenders. Adidtionally, the Environmental Defenders connected with Save The Tigris to build a common team of lawyers to advocate for the protection of Iraqi activists.
(5th day) ICSSI GENERAL ASSEMBLY
The ICSSI General Assembly is a space dedicated to the internal review of ICSSI working strategies and structure.
On the 16th of March, approximately 20 representatives from some of the main partners of ICSSI attended the General Assembly session, sharing their perspectives on how to improve the work of ICSSI supporting Iraqi civil society. The ICSSI Coordinators presented the results of the Strategic Review, which was carried out by the ICSSI Secretariat from 2020 to the end of 2021 to reflect accurately the work done inside the ICSSI and to identify principles, rules, and means to improve its internal processes and work.
The Participatory Democracy system and system of taking decisions by positive consent has been reviewed and agreed on in a special document.
The new Mission Statement has been collectively reviewed and finally approved, together with the ICSSI Consensus Charter.
The ICSSI Mission Statement states ICSSI's identity, aim, history, values, principles, and core thematic issues of its work.
The ICSSI Consensus Charter, explains how to put into practice the principle of participatory democracy within the ICSSI decision-making processes following the consensus methodology, enhancing collective and inclusive decisions.
The new ICSSI Internal Regulations have been collectively reviewed and approved.
The ICSSI Internal Regulations establish the internal structure of ICSSI, its primary decision-making bodies, how to regulate its staff, volunteers, coordinating NGO, partnerships, and campaigning processes.
The ICSSI Assembly of Members has been constituted, collecting members' willingness to become part of it and their representative's participation.
The ICSSI Assembly of Members is the new political body of the ICSSI, in charge of guiding its activities and supervising its coherence with ICSSI values and principles as stated in the Mission Statement, and the effective implementation of the ICSSI Strategy as established by the ICSSI Conference.
The ICSSI Secretariat – the implementation body of the ICSSI- has been dissolved and renewed with the participation of new members.
The old co-coordinators have resigned, giving space to intergenerational change: Silvia Abbà has been nominated as the new International Coordinator, while a selection process has been opened to collecting candidacies for the Iraqi Coordinator position.
Women Trade Unionists and Working Women in Iraq Today!
Draught, and Misuse threaten the natural and cultural heritage, and the right of access to water for the inhabitants of Mesopotamia
Between the Laws Inherited from the Era of Dictatorship and Legislation Seeking to Restrict Freedom of Expression and the Press in Iraq, The Reality is Not Consistent with the Principles of Democracy


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