With a stay at Guesthouse Belvedere in Patong (Nanai Road), you'll be minutes from Bazaan Fresh Market and Banzaan Fresh Market. This hotel is within close proximity of Jungceylon Shopping Center and Royal Paradise Night Market.
Make yourself at home in one of the 33 air-conditioned rooms featuring refrigerators and minibars. Complimentary wireless Internet access keeps you connected, and cable programming is available for your entertainment. Bathrooms have showers and complimentary toiletries. Conveniences include safes and desks, and housekeeping is provided daily.
Satisfy your appetite with Italian cuisine at Bucintoro, a restaurant which features a bar. Dining is also available at the coffee shop/café. Cooked-to-order breakfasts are available daily from 9 AM to 1 PM for a fee.


No doubt you are planning your holidays if you have clicked on this site. Would you like to find out as much information as possible as a prospective visitor of ours and ensure that your well-planned stay here is untroubled and cloudless? We are ready to help you; we have collected all the useful hints and tips you might need to be familiar with when you arrive in our town.
If you come here just for a one-day visit, an important starting point could be the car park in the town centre, where we have introduced reduced parking fees this year for the safety of your car even for all day. The spa and thermal lake are just a five-minutes' walk from here. You must not skip bathing in the lake as it offers you an unforgettable experience in winter and summer alike.
Should you need any up-to-date information, just pop in the Tourinform Office, where you can get further useful hints on the leisure opportunities; events, places of interest in the area and some other services.
As for a program after bathing, we recommend our restaurants to your attention where you can also taste the specialties of Zala gastronomy. After a substantial dinner you should take a walk in the inner town or join a historic sightseeing tour, or perhaps you could take a "Dotto" sightseeing train to look around. You may interrupt the "Dotto" sightseeing in Egregy where your family members (except children and the driver on your way home) can make the day in Hévíz richer in experiences by wine tasting in the winery row.
No matter which season you choose to come for a holiday in Hévíz, before leaving home you should browse our booklet of the local events; the spa concerts, shows and seasonal festivals offer you to have great fun.
With regard to all these, we believe that you'd rather come and stay in Hévíz for longer than one or two days so that you will have a chance to experience each opportunity both of the active and passive ways of recreation. The hotels in Hévíz await their guests with a wide range of services of high standard. You can make your choice from a rich variety of 3, 4 and 5-star hotels or private guest houses with an atmosphere of intimacy. The services of the Hévíz hotels and guest houses include curative treatment, health-giving therapy, wellness recreation, family relaxation and exercise programs equally.
Visit our office, where you can buy many "Hévíz marked" products as a gift. If you don't have any time to get there during your vacation, you can order these products from our webshop.


An overlay or table runner simply won't look beautiful without a proper tablecloth to go underneath. Our 72" by 144" pieces can cover your 96" by 30" banquet tables with ease. The covering you choose must serve three main purposes. The first is to protect the table surface from messes and wear. The second is to create an eye-catching presentation for guests. And the third is to provide your guests with a comfortable space to sit during the event. Our tablecloths offer all that and more!
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We offer maximum customization with each tablecloth order. You can choose custom hems and colors. To begin, simple click the link above or the "Colors" tab to get a view of our extensive dye options. We can show a color for every mood, personality or theme with rich gold, fiery red, delicate pink and traditional white and black. Many more hues are available and ready to be used at your next event!


the smoke detector in the kitchen goes off when you burn the food. this is good if you left the room and are watching tv. but if you are racing around cooking different things and trying to pull burning food off the stove the last thing you want is to hear the alarm. this modified alarm would only be armed if it is not detecting movement. it should not be so sensitive to movement that sleeping keeps it from working.
You sleep in the kitchen?
You need to be sure that the motion detector can't be triggered by visible flames, flying sparks, moving masses of hot air, or curtains being blown around. You could do this with a camera hooked to a computer with software to do facial recognition. It could be programmed to shut down the alarm if it sees a face looking straight at it. If the computer is off, it would just keep making noise.


text:
Q: Using "exec" to Update a Table I have a temp table named as #temp with 2 columns:
clientID (varchar),
result (int)

I just want to loop in it and check the clientID with a stored procedure which takes 2 varchar parameters and returns 0 or 1.
I coded:
update #temp set result=exec sp_x 'clientID' '@clientID'

clientID is the column name of #temp.
@clientID comes from parameter of the main SP
It comes up with a warning:

Incorrect syntax near the keyword 'exec'.

So, what to do?
Thanks in advance...

A: You need to call your procedure inside a loop
declare @id varchar(10)
declare @result int
declare looper cursor for select clientID, result from #temp

fetch next from looper
into @id, @result

-- loop on #temp table
open looper
while @@fetch_status = 0
begin
  -- call your procedure and store the result into a variable
  -- do what ever you need to do

end

close looper
deallocate looper

redpajama_set_name: RedPajamaStackExchange


Yay! You're now following raymarine fishfinder in your .
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If the signal doesn't encounter anything along the way, it reaches the bottom. Soft bottoms like mud and weeds tend to absorb the signal. Hard bottoms such as rock reflect a stronger signal back.
- All Raymarine fishfinders operate using Sonar.
– Determines the depth a sonar can reach.
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Forum: Threads: Posts: Last Post: ..
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© Shop and read reviews about Raymarine Fishfinders at West Marine. Get free shipping on all orders to any West Marine Store near you today.


text:
Alan Andrew Watson FRS (Edimburgo, ) é um físico britânico. É professor emérito da Universidade de Leeds.

Watson estudou na Universidade de Edimburgo (BSc 1960) e recebeu um PhD em 1964, com a tese Physics of Condensation of Water Vapour.

Watson foi professor de física da Universidade de Leeds em 1984, tendo sido previamente Reader de física de partículas cósmicas, e aposentado em 2003 como professor emérito.

Watson foi instrumental na criação do Observatório Pierre Auger na Argentina (início 1999), que reuniu os dados que levaram a grandes descobertas em astronomia de raios cósmicos. O observatório cobre uma área de 3000 km2 com 1600 detectores de partículas cada um colocado a intervalos de 1,5 km.

Watson foi eleito Membro da Royal Society (FRS) em 2000.

Ligações externas
Curriculum Vitae

Membros da Royal Society
Professores da Universidade de Leeds
Físicos do Reino Unido
Astrónomos do Reino Unido
Alunos da Universidade de Edimburgo
Naturais de Edimburgo

redpajama_set_name: RedPajamaWikipedia


text:
\section{Introduction}

Ever since the classic result of \ac{sw}~\cite{Seiberg:1994rs}, $\mathcal{N}=2$ gauge theories have occupied a prominent place in theoretical physics. The resulting low energy \ac{sw} effective action  is given in terms of a Riemann surface, the \ac{sw} curve, which encodes all the perturbative and non-pertubative quantum effects of the gauge theory. While all the perturbative corrections had been known since~\cite{Gates:1981yc,Howe:1983wj,Seiberg:1988ur}, this solution gave a prediction for an infinite number of non-perturbative instanton corrections, the first few terms of which could be checked by explicit computation~\cite{Dorey:1996hu,Dorey:1996bf}.

Not long afterwards, M--theory was developed as an eleven-dimensional non-per\-tur\-ba\-tive completion of String Theory. In a striking paper  Witten showed how the \ac{sw} curve could be naturally obtained from the geometry of intersecting  \NS5 and \D4--branes lifted to M--theory where they become a single \M5--brane~\cite{Witten:1997sc}. Moreover the complete quantum \ac{sw} effective action for $\mathcal{N} = 2$ supersymmetric $SU(N)$ Yang--Mills theory was obtained in~\cite{Howe:1997eu} from the classical dynamics of the \M5--brane.

An alternative method to compute the \ac{sw} solution from first principles came with Nekrasov's seminal paper using the $\Omega$--background~\cite{Nekrasov:2002qd}. This background deforms the gauge theory and allows for localization techniques to be used to compute all the instanton corrections and also reconstruct the curve and its associated quantities~\cite{Nekrasov:2003rj}. Since then the $\Omega$--background has received a lot of interest, most recently in the context of the correspondence by Alday, Gaiotto and Tachikawa~\cite{Alday:2009aq} and work related to it.

The so-called \emph{fluxtrap} background~\cite{Hellerman:2011mv,Reffert:2011dp,Hellerman:2012rd} provides a string-theoretical construction of the Euclidean  $\Omega$--background determined by a  two-form $\omega = \di U$.\footnote{See~\cite{Fucito:2011pn,Antoniadis:2013bja} for alternative realizations.} In particular the bosonic  Abelian worldvolume  action for   \D4--branes suspended between  \NS5--branes in this background was given in \cite{Hellerman:2012zf}. The generalization to non-Abelian fields is given by ($\mu,\nu=0,1,2,3$)
\begin{multline}
  \label{action}
  \mathscr{L}_{\D4} = \frac{1}{g^2_4} \Tr \Big[\frac{1}{4} \mathbf{F}_{\mu\nu} \mathbf{F}_{\mu\nu} +  \frac{1}{2}(\mathbf{D}_\mu \, \boldsymbol{\varphi} + \frac{1}{2} \mathbf{F}_{\mu\lambda}\hat U^\lambda)(\mathbf{D}_\mu \, \bar{\boldsymbol{\varphi}}  + \frac{1}{2}\mathbf{F}_{\mu\rho}\hat U^\rho) \\
- \frac{1}{4}[\boldsymbol{\varphi}, \bar{\boldsymbol{\varphi}}]^2+ \frac{1}{8}(\hat U^\mu \mathbf{D}_\mu (\boldsymbol{\varphi}-\bar{\boldsymbol{\varphi}}))^2\Big] \ ,
\end{multline}
where a hat denotes the pull-back to the brane and a bold-face indicates a non-Abelian field.
 The \emph{fluxtrap} can be lifted to M--theory~\cite{Hellerman:2012zf}. At order $\epsilon$ it is given by  ($M,N=0,1,2,...,10$)
\begin{subequations}
  \label{eq:first-order-Mbulk}
  \begin{align}
     g_{MN} &= \delta_{MN} + \mathcal{O}(\epsilon^2) \, ,\\
    G_4 &= \left( \di z + \di \bar z  \right) \wedge \left( \di s + \di \bar s \right) \wedge \omega\, ,
  \end{align}
\end{subequations}
where \( s = x^6 + \im x^{10} \), \( z = x^8 + \im x^9 \), and
\begin{equation}
  \omega = \epsilon_1 \di x^0\wedge \di x^1 + \epsilon_2 \di x^2\wedge \di x^3 + \epsilon_3 \di x^4 \wedge \di x^5 \ .
\end{equation}
The background has 8 Killing spinors if \( \epsilon_1 + \epsilon_2 + \epsilon_3 = 0 \), and 16 Killing spinors in the special case \( \epsilon_1 = - \epsilon_2 \) and \( \epsilon_3 = 0 \).\footnote{The $\epsilon_3$ component, although generically non-vanishing, will not play a role in this paper as the \M5--brane will be held fixed in the $x^4,x^5$ plane.}

In this paper we will derive the corrections to first order in $\epsilon$ to the $\Omega$--deformed \ac{sw} action. We do this by employing the M--theory lift of the fluxtrap background. As we will see, the classical M--theory calculation has the invaluable benefit of giving a quantum result in gauge theory since in this case, the result is independent of the effective coupling in the gauge theory. We embed the \M5--brane in the $\Omega$-background and study the most supersymmetric configuration which to first order in $\epsilon$ is still of the form $\setR_4 \times \Sigma$ with an additional self-dual three-form. %
This is the ground state of a six-dimensional theory on top  of which we have fluctuations fulfilling some assumptions detailed in the following. %
These fluctuations obey \emph{scalar} and \emph{vector equations of motion} that arise from the six-dimensional theory, where the scalar equation encodes the fact that the M5--brane is a (generalized) \emph{minimal surface} and the vector equation posits that the self-dual three-form on the brane is the (generalized) \emph{pullback of the three-form field in the bulk}. To arrive at the four-dimensional gauge theory, we must integrate these equations over the Riemann surface $\Sigma$ %
using an appropriate measure.
The integration results in one vector equation and two scalar equations in four dimensions, which are the Euler--Lagrange equations for a four-dimensional action, which in the case $\epsilon=0$ reproduces the undeformed \ac{sw} action.
We explicitly treat the case of \( SU(2) \) without matter, however there is a natural generalization of our result to any gauge group and matter content.

\bigskip
The plan of this paper is as follows. In Section~\ref{sec:m5} we describe the embedding of the \M5--brane, the six-dimensional equations of motion and their reduction to four-dimensions. We also give an action that captures these equations of motion. This action can be extrapolated to second order in $\epsilon$ and  generalized to arbitrary gauge group and matter content. In Section~\ref{sec:conclusions} we give our conclusions. We also provide an appendix that gives some technical steps in the evaluation of various non-holomorphic integrals over the Riemann surface that arise.

\section{M5--brane dynamics in the $\Omega$--fluxtrap}\label{sec:m5}

\paragraph{The homogeneous embedding of the \M5--brane.}

 Due to the fundamentally Euclidean nature of the fluxtrap background, we will be discussing the Euclidean version of \ac{sw}-theory. For this reason, the self-duality condition for the three-form \( h_3 \) on the \M5--brane turns into
\begin{equation}
    \im*_6 h_3 =  h_3 \,,
\end{equation}
which we will refer to as \emph{self-duality}.

The embedding of the \M5--brane in the fluxtrap background at order \( \epsilon \) has already been discussed in~\cite{Hellerman:2012zf}, where it was found that the brane wraps a Riemann surface. Let us recall here the argument.
As discussed in~\cite{Witten:1997sc}, the M--theory lift of a \NS5--\D4 system (extended respectively in \( x^0, \dots, x^3, x^8, x^9 \) and \( x^0, \dots, x^3, x^6 \)) is a single \M5--brane extended in \( x^0, \dots, x^3 \) and wrapping a two-cycle in \( x^6, x^8, x^9, x^{10} \). We use static gauge and assume that the \M5--brane has coordinates $x^\mu$, $\mu=0,1,2,3$ and $z=x^8+\im x^9$. We also assume that the only non-vanishing  scalar field is $s = x^6+\im x^{10}$. The precise form of the embedding is found if we require this brane to preserve the same supersymmetries of the original \tIIA system. Given the Killing spinors \( \eta_0 \) of the bulk, the \M5--brane preserves those satisfying~\cite{Howe:1996yn,Howe:1997fb} ($m,n=0,1,2,...,5$)
\begin{align}
  \proj{\M5}_- \eta_0 &= \tfrac{1}{2} \left( 1 - \Gamma_{\M5}  \right)  \eta_0 = 0 \ , &
  \Gamma_{\M5} &= -\frac{\epsilon^{m_1 \dots m_6} \hat \Gamma_{m_1 \dots m_6} }{6! \sqrt{\hat g}}
  \left( 1 - \tfrac{1}{3} \hat \Gamma^{n_1 n_2 n_3} h_{n_1 n_2 n_3} \right)  \ ,
\end{align}
where \( \hat \Gamma \) and \( \hat g \) are the gamma matrices and the metric, pulled back to  the brane. Here \( h_3 \) is the self-dual three-form on the \M5--brane worldvolume which satisfies
\begin{equation}
  \di H_3 = - \tfrac{1}{4}  \hat G_4 \,,
\end{equation}
where $H_3 = h_3 + {\mathcal O}(h_3^3)$.

For \( \epsilon = 0 \) we have $h_3=0$ and the \M5--brane is described by a Riemann surface \( \bdel s = 0 \)~\cite{Witten:1997sc}.
Let us now consider the first order effect that arises when turning on $\epsilon$. To this order we may simply take $H_3=h_3$ but in principle $s$ may pick up a non-holomorphic piece. However at ${\mathcal O}(\epsilon)$
the pullback  only  depends holomorphically on \( s (z) \) since \( \hat \omega \) is by itself of order \( \epsilon \):
\begin{equation}
  \hat G_4  = - \left( \del s  - \bdel \bar s  \right) \di z \wedge \di \bar z \wedge \hat\omega+{\mathcal O}(\epsilon^2)\, .
\end{equation}
Therefore we can take
\begin{equation}
  h_3 = \tfrac{1}{4} \left( \bar s  - \bar z \del s  + f(z)  \right) \di z \wedge \hat\omega^- + \tfrac{1}{4}  \left(  s  -  z \bdel \bar s  + \bar f(\bar z) \right) \di \bar z \wedge \hat\omega^+ \, ,
\end{equation}
where $f$ is an arbitrary holomorphic function and we have decomposed the two-form \( \hat\omega \) as
\begin{equation}
\begin{aligned}
  \hat\omega &= \frac{\epsilon_1 + \epsilon_2}{2} \left( \di x^0 \wedge \di x^1 + \di x^2 \wedge \di x^3 \right) + \frac{\epsilon_1 - \epsilon_2}{2}  \left( \di x^0 \wedge \di x^1 - \di x^2 \wedge \di x^3 \right) \\
  &= \hat\omega^+ + \hat\omega^- \, .
\end{aligned}
\end{equation}
These are all the ingredients needed to write the supersymmetry condition,
\begin{equation}
  \proj{\M5}_- \eta = \proj{\M5}_- \proj{\NS5}_+ \proj{\D4}_+ \eta_0 = 0\,,
\end{equation}
where the projectors \( \proj{\NS5} \) and \( \proj{\D4} \) refer to the \M5--branes resulting from the lift of the \NS5--brane and \D4--brane introduced above such that \( \eta = \proj{\NS5}_+ \proj{\D4}_+ \eta_0 \) are the Killing spinors preserved by the branes. Since the two \M5--brane projectors commute, the full configuration preserves two supercharges in the generic case and four if \( \epsilon_1 = - \epsilon_2 \).  An explicit calculation shows that the condition is satisfied at ${\mathcal O}(\epsilon)$ if
\begin{equation}
  \begin{cases}
    \bdel s   = 0\ , \\
    f(z) = 0 \ ,
  \end{cases}
\end{equation}
which completely fix the embedding of the \M5--brane and the self-dual field \( h_3 \).

Thus even at order \( \mathcal{O}(\epsilon) \) the brane is embedded holomorphically in spacetime. For the simplest case corresponding to pure $SU(2)$ Yang--Mills, the precise form was found in~\cite{Witten:1997sc} and is determined implicitly by
\begin{align}
  t^2- 2B(z | u)t + \Lambda^4 &= 0 \ , & t &= \Lambda^2e^{- s/R}
 \ ,
\end{align}
where  \( B(z | u) = \Lambda^4z^2 - u\), $\Lambda$ is a mass scale and $R$ the radius of the $x^{10}$-direction. This embedding defines a Riemann surface $\Sigma$ with modulus \( u \),
\begin{equation}
  \Sigma = \set{(z,s)| s = s(z|u)} .
\end{equation}
It is useful to observe that
\begin{equation}
 \frac{ \del s}{\del u} \di z= -\frac{1}{2\Lambda^4z} \frac{ \del s}{\del z} \di z =   \frac{R \di z}{\sqrt{Q(z|u)}} =  R\lambda
\end{equation}
is the unique holomorphic one-form on $\Sigma$
where  \( Q(z|u) = B(z|u)^2 - \Lambda^4 \).  For most of this paper we will simply set $R=\Lambda=1$. They are in principle needed on dimensional grounds, since both $s$ and $z$ have dimensions of length whereas the modulus $u$ is usually taken to have mass-dimension two. We will briefly reinstate them in the conclusions by simply rescaling $z$ and $s$, when discussing the quantum nature of our result.

\paragraph{Equations of motion in 6d.}

Having found the embedding of the \M5--brane we want to describe the low-energy dynamics of the fluctuations around the equilibrium. In fact, since we are interested in the effective four-dimensional theory living on \( x^0, \dots, x^3 \) which results from integrating the \M5 equations of motion over the Riemann surface \( \Sigma \), we will assume that:
\begin{enumerate}
\item the geometry of the five-brane is still a fibration of a Riemann surface over \( \setR^4 \);
\item for each point in \( \setR^4 \) we have the same Riemann surface as above, but with a different value of the modulus \( u \).
\end{enumerate}
In other words, the modulus \( u \) of \( \Sigma \) is a function of the worldvolume coordinates and the embedding is still formally defined by the same equation, but now \( s = s ( z | u(x^\mu)) \) so that the \( x^\mu \)--dependence is entirely captured by
\begin{equation}
  \label{eq:xmu-dependence}
  \del_\mu s (z | u (x^\mu)) = \del_\mu u \frac{\del s}{\del u} \,.
\end{equation}
For ease of notation we will drop in the following the explicit dependence of \( s \) on \( u(x^\mu) \) and write directly \( s = s (z, x^\mu) \). Much of our discussion follows the undeformed case considered in detail in~\cite{Howe:1997eu,Lambert:1997dm,Lambert:1997he}.

The dynamics can be obtained by evaluating the \M5--brane equations of motion. Here we will only focus on the bosonic fields. Covariant equations of motion for the \M5--brane were obtained in~\cite{Howe:1996yn,Howe:1997fb}. In general these are rather complicated equations, particularly with regard to the three-form. However in this paper we only wish to work to linear order in $\epsilon$ and quadratic order in spatial derivatives $\del_\mu$. In particular we can take $H_3=h_3$ and the equations of motion reduce to\footnote{Note that we have chosen the opposite sign to the \emph{rhs} of the scalar equation as compared to what is given in~\cite{Howe:1997fb}. This corresponds to a choice of brane or anti-brane.}
\begin{align}
\label{eq:general-scalar-equation}
 \left( \hat g^{mn} - 16 h^{mpq}h^n{}_{pq} \right) \nabla_m \nabla_n X^{I} &=  -\frac{2}{3 }  \hat G\indices{^{I}_{mnp}} h^{mnp} \,, \\
  \di h_3 &= - \tfrac{1}{4} \hat G_4 \,,
\end{align}
where $I = 6,\dots,10$ and the geometrical quantities are defined with respect to  the pullback of the spacetime metric to the brane ${\hat g}_{mn}$.

As a first step we need to write the three-form field on the brane. In full generality, \( h_3 \) can be decomposed as
\begin{equation}
  h_3 = - \tfrac{1}{4} \left( \hat C_3 + \im *_6 \hat C_3 - \Phi \right)  \, ,
\end{equation}
where \( \hat C_3 \) is the pullback of the three-form in the bulk, and \( \Phi \) is a self-dual three-form that will encode the fluctuations of the four-dimensional gauge field.

Since we ultimately want to discuss the gauge theory living on the worldvolume coordinates \( x^0, \dots, x^3 \), we make the following self-dual ($\im*_6 \Phi =   \Phi$) ansatz for \( \Phi \):
\begin{equation}
  \begin{aligned}
    \Phi ={}&\frac{ \kappa}{2}\cF_{\mu\nu}\di x^\mu\wedge \di x^\nu\wedge\di z+ \frac{\bar \kappa}{2}\wt{\cF}_{\mu\nu}\di x^\mu\wedge \di x^\nu\wedge\di \bar z\\
    & +  \frac{1}{1+|\del s|^2}\frac{1}{3!}\epsilon_{\mu\nu\rho\sigma}\left(  \del^\tau s \bdel \bar s \, \kappa \cF_{\sigma\tau}-\del^\tau\bar s\del s \, \bar\kappa \wt{\cF}_{\sigma\tau} \right)\di x^\mu\wedge\di x^\nu\wedge\di x^\rho \,.
  \end{aligned}
\end{equation}
The two-form \( \cF \) is anti-self-dual in four dimensions, while \( \wt{\cF} \) is self-dual:
\begin{align}
 *_4 \cF &= - \cF \,, & *_4 \wt{\cF} &= \wt{\cF} \,.
\end{align}
Here $*_4$ is the flat space Hodge star and \( \kappa(z) \) is a holomorphic function given by~\cite{Lambert:1997dm}
\begin{equation}
  \kappa = \frac{\di s}{\di a} =
  \left( \frac{\di a}{\di u}  \right)^{-1} \lambda_z \, .
\end{equation}
Here $\lambda = \lambda_z dz$ is the holomorphic one-form on $\Sigma$ and \( a \) is the scalar field used in the Seiberg--Witten solution and related to $\lambda$ by
\begin{equation}
  \frac{\di a}{\di u} = \oint_A \lambda\ ,
\end{equation}
where $A$ is the a-cycle of $\Sigma$. In the following,  ${\cF}$ and $\wt{\cF}$ will be related to the four-dimensional gauge field strength, thus justifying our ansatz.

We also need to choose a gauge for the three-form potential \( C_3 \) in the bulk:
\begin{equation}
    C_3 = -\tfrac{1}{2} \left(\bar s\di v-\bar v\di s+s\di v-\bar v \di \bar s\right)\wedge\omega+\mathrm{c.c}.
\end{equation}
Its pullback on the Riemann surface $\set{ v = z, s = s(z, x^\mu)}$ is given by
\begin{equation}
  \hat C_3 = -\tfrac{1}{2} \left(\bar s\di z-\bar z\del s\di z-\bar z\del_\mu s\di x^\mu+s\di z-\bar z \bdel \bar s\di\bar z-\bar z\del_\mu\bar s\di x^\mu\right)\wedge\hat\omega + \text{c.c.} \, .
\end{equation}
We are only interested in terms up to second order in the spacetime derivatives \( \del_\mu \) and in particular we observe that \( \hat\omega \) is by itself of first order. It follows that the six-dimensional Hodge dual is given by
\begin{equation}
  \begin{aligned}
    \im *_6\hat C_3 ={}& \tfrac{1}{2} \left(\bar s\di z-\bar z\del s\di z+s\di z+\bar z\bdel s\di\bar z - s \di \bar z + z \bdel\bar s \di\bar z - \bar s \di\bar z - z \del s \di z \right) \wedge \dual{\hat \omega}\\
    &   +\frac{1}{2\cdot 3!}\left( 1 + \abs{\del s}^2 \right)\epsilon_{\mu\nu\lambda\rho}C^{\mu\nu\lambda} \di x^\rho\wedge\di z\wedge \di\bar z \\
    &  +\frac{1}{1+\abs{\del s}^2}\epsilon_{\mu\nu\rho\sigma}\left(\del^\tau s \bdel \bar s \hat C_{\sigma \tau z} -  \del^\tau\bar s\del
      s   \hat C_{\sigma\tau\bar z} \right) \di x^\mu \wedge \di x^\nu \wedge \di x^\rho \ ,
  \end{aligned}
\end{equation}
where \( \dual{\hat\omega} = *_4 \hat\omega = \hat\omega^+ - \hat\omega^- \).

\paragraph{The vector equation.}

Consider now the vector equation \( \di h_3 = - \frac{1}{4} \hat H_4  \). Given our expression for \( h_3 \), the equation becomes
\begin{equation}
  \di \Phi = \im \di *_6 \hat C_3  \ ,
\end{equation}
where we see explicitly the role of the bulk three-form as source for the gauge field on the brane.
At this point it is useful to quickly discuss  the issue of gauge covariance of the three-form equation. The bulk three-form is defined up to the differential of a two-form \( C_3 \mapsto C'_3 + \di B_2 \). Under this shift the vector equation becomes
\begin{equation}
  \di \Phi =  \im  \di *_6 \hat C_3' + \im \di *_6 \di \hat B_2  \ ,
\end{equation}
which can be compensated for by an analogous shift in the fluctuations:
\begin{equation}
  \Phi \mapsto \Phi' + \di \hat B_2 + \im *_6 \di \hat B_2 \,.
\end{equation}

\bigskip

Let us go back to our ansatz. The tensor \( \Phi \) does not contribute to the \( \mu\nu z \bar z \) component:
\begin{equation}
   \left.\di \Phi \right|_{\mu\nu z\bar z} \equiv 0
\end{equation}
so we only need to verify that
\begin{equation}
  \left. \di *_6 \hat C \right|_{\mu\nu z\bar z} = 0 \, ,
\end{equation}
which is satisfied up to terms of order $\mathcal{O} (\del_\mu)^3 $, taking into account the fact that $\hat\omega$ is by itself of order $\mathcal{O}(\del_\mu) $. Similarly, also the \( \mu\nu \lambda\rho\) component of the equation of motion is of higher order.

It is convenient to take the six-dimensional dual of the remaining terms and decompose them in coordinates:
\begin{equation}
  *_6\di (\Phi - \im *_6 \hat C_3) =  \tfrac{1}{2}E_{\mu z} \di x^\mu \wedge \di z +   \tfrac{1}{2}E_{\mu \bar z} \di x^\mu \wedge \di \bar z = 0 \, ,
\end{equation}
where explicitly
\begin{subequations}
  \begin{align}
    E_{\mu z} &= \del_\mu ( \kappa \cF_{\mu \nu }- \hat C_{\mu \nu z}) + \del \left[ \frac{\bdel \bar s \del_\nu s}{1 + \abs{\del s}^2} ( \kappa \cF_{\mu\nu} - \hat C_{\mu\nu z}) \right] - \del \left[ \frac{\del s \del_\nu \bar s}{1 + \abs{\del s}^2} ( \bar \kappa \wt{\cF}_{\mu\nu} - \hat C_{\mu\nu \bar z} )\right] \, , \\
    E_{\mu \bar z} &= \del_\mu ( \bar \kappa \wt \cF_{\mu \nu } - \hat C_{\mu \nu \bar z}) + \bdel \left[ \frac{\del s \del_\nu \bar s}{1 + \abs{\del s}^2} ( \bar \kappa \wt{\cF}_{\mu\nu} - \hat C_{\mu\nu \bar z}) \right] - \bdel \left[ \frac{\bdel \bar s \del_\nu s}{1 + \abs{\del s}^2} ( \kappa {\cF}_{\mu\nu} - \hat C_{\mu\nu z} )\right] .
  \end{align}
\end{subequations}
Note that because of the epsilon tensors in the definition of \( E_{\mu z} \), the equations only depend on \( \hat\omega \) and not on \( \dual{\hat\omega} \).

To obtain the equations of motion of the vector zero-modes in four dimensions we need to reduce these equations on the Riemann surface. In order for the integral to be well-defined everywhere on \( \Sigma \) we have only two possible choices for the integrand, depending on the (unique) one-form \( \lambda \) or its complex conjugate:
\begin{subequations}
  \label{eq:integral-vector-equation}
  \begin{align}
    \int_\Sigma *_6  \di (\Phi - \im \di * \hat C_3) \wedge \bar \lambda &= \di x^\mu \wedge \int_\Sigma E_{\mu z} \di z \wedge \bar \lambda = 0 \, ,\\
    \int_\Sigma *_6 \di (\Phi - \im \di * \hat C_3) \wedge \lambda &=
    \di x^\mu \wedge \int_\Sigma E_{\mu \bar z} \di \bar z \wedge \lambda = 0
    \, .
  \end{align}
\end{subequations}
The explicit integration is relatively straightforward using the techniques explained in Appendix~\ref{sec:line-integrals}. The only non-vanishing integrals have been already evaluated in~\cite{Howe:1997eu,Lambert:1997he}:
\begin{align}
  I_0 &= \int_\Sigma \lambda \wedge \bar \lambda = \frac{\di a }{\di u}
  \left( \tau - \bar \tau \right) \frac{\di \bar a}{\di \bar u} \, ,\\
  K &= \int_\Sigma \bdel
  \left[ \frac{\lambda_z \bdel \bar s}{1 + \abs{\del s}^2} \right] \di \bar z \wedge \lambda = -
  \left( \frac{\di a }{\di u} \right)^2 \frac{\di \tau}{\di u} \, ,
\end{align}
where one uses the following definitions:
\begin{align}
  a &= \oint_A \lambda_{SW} \, , & a_D &= \oint_B \lambda_{SW} \, , & \tau &= \frac{\di a_D}{\di a} \, , & \lambda &= \frac{\del \lambda_{SW}}{\del u} \, ,
\end{align}
along with the Riemann bi-linear identity
\begin{equation}
\int \lambda\wedge \bar \lambda = \oint_B\lambda\oint_A\bar\lambda - \oint_A\lambda\oint_B\bar\lambda\;.
\end{equation}
The two integrals in Eq.~\eqref{eq:integral-vector-equation} become
\begin{subequations}
  \label{eq:integrated-vector-equations}
  \begin{align}
    \left( \tau - \bar \tau \right)
    \left( \del_\mu \cF_{\mu\nu} + \del_\mu a \, \hat\omega_{\mu\nu} \right) + \del_\mu \tau \cF_{\mu \nu} - \del_\mu \bar \tau \wt{\cF}_{\mu\nu} &= 0 \, ,\\
    \left( \tau - \bar \tau \right) \left( \del_\mu \wt{\cF}_{\mu\nu}
      + \del_\mu \bar a \, \hat\omega_{\mu\nu} \right) + \del_\mu \tau
    \cF_{\mu \nu} - \del_\mu \bar \tau \wt{\cF}_{\mu\nu} &= 0 \, .
  \end{align}
\end{subequations}
Taking the difference of the two equations we find
\begin{equation}
  \label{eq:difference-vector-equations}
  \del_\mu ( \cF_{\mu\nu} - \wt{\cF}_{\mu\nu}) = - \del_\mu \left( a - \bar a \right) \hat\omega_{\mu\nu} \, ,
\end{equation}
which is solved by writing
\begin{equation}
  \begin{cases}
    \cF = \left( 1 - * \right) F - \left( a - \bar a \right) \hat\omega^- \,,\\
    \wt{\cF} = \left( 1 + * \right) F + \left( a - \bar a \right) \hat\omega^+\,,
  \end{cases}
\end{equation}
where \( F \) satisfies the standard Bianchi identity
\begin{equation}
  \di F = 0 \, ,
\end{equation}
and can be written as the differential of a one-form \( F = \di A \). In the following we will identify \( F \) with the four-dimensional gauge field and, in this sense, Eq.~\eqref{eq:difference-vector-equations} represents the correction to the Bianchi equations introduced by the \( \Omega \)--deformation. Substituting this condition into the first equation of~\eqref{eq:integrated-vector-equations}, we derive the final form of the four-dimensional vector equations:
\begin{multline}
  \label{eq:vector-equation}
  \left( \tau - \bar \tau \right) \left[ \del_\mu F_{\mu\nu} + \tfrac{1}{2} \del_\mu ( a + \bar a ) \hat\omega_{\mu\nu} + \tfrac{1}{2} \del_\mu (a - \bar a) \dual{\hat\omega}_{\mu\nu} \right] \\+ \del_\mu \left( \tau - \bar \tau\right) \left[ F_{\mu\nu} + \tfrac{1}{2} \left( a - \bar a \right) \dual{\hat\omega}_{\mu\nu} \right]  %
  - \del_\mu
  \left( \tau + \bar \tau \right) \left[ \dual{F}_{\mu\nu} + \tfrac{1}{2} \left( a - \bar a \right)  \hat\omega_{\mu\nu} \right] = 0 \, ,
\end{multline}
where \( \dual{F} = *_4 F \).

\paragraph{The scalar equation.}

Next we turn our attention to evaluating the scalar equation.   The main new ingredient with respect to the calculation in the literature ~\cite{Lambert:1997dm} is the presence of a \emph{rhs} term in Equation~\eqref{eq:general-scalar-equation}, which reads
\begin{equation}
  -\frac{2}{3 } \hat G\indices{^{I}_{mnp}} h^{mnp}
  = \frac{2}{ 1 + \abs{\del s}^2}\hat\omega^-_{\mu\nu} \cF_{\mu\nu} \left( \frac{\di a}{\di u}  \right)^{-1} \lambda_z + \frac{2}{ 1 + \abs{\del s}^2} \hat\omega^+_{\mu\nu} \wt{\cF}_{\mu\nu} \left( \frac{\di \bar a}{\di \bar u}  \right)^{-1} \bar \lambda_{\bar z} \ ,
\end{equation}
for both non-trivial cases \( X^{I} = s \) and \( X^{I} = \bar s \). The two corresponding scalar equations take the form
\begin{align}
  E &
  \begin{multlined}[t][.8\textwidth]
    =\del_\mu \del_\mu s - \del \left[ \frac{\del_\rho s\del_\rho s \bdel \bar s }{1 + \abs{\del s}^2} \right] - \frac{16 \del^2 s}{\left( 1 + \abs{\del s}^2 \right)^2}h_{\mu\nu \bar z} h_{\mu\nu \bar z}  \\
    -2\hat\omega^-_{\mu\nu} \cF_{\mu\nu} \left( \frac{\di a}{\di u}
    \right)^{-1} \lambda_z + 2 \hat\omega^+_{\mu\nu}
    \wt{\cF}_{\mu\nu} \left( \frac{\di \bar a}{\di \bar u}
    \right)^{-1} \bar \lambda_{\bar z} = 0 \, ,
  \end{multlined}\\
  \bar E &
  \begin{multlined}[t][.8\textwidth]
    = \del_\mu \del_\mu \bar s - \bdel \left[ \frac{\del_\rho \bar s \del_\rho \bar s \del s }{1 + \abs{\del s}^2} \right] - \frac{16 \bdel^2 \bar s}{\left( 1 + \abs{\del s}^2 \right)^2}h_{\mu\nu z} h_{\mu\nu z}  \\
    -2\hat\omega^-_{\mu\nu} \cF_{\mu\nu} \left( \frac{\di a}{\di u}
    \right)^{-1} \lambda_z + 2 \hat\omega^+_{\mu\nu}
    \wt{\cF}_{\mu\nu} \left( \frac{\di \bar a}{\di \bar u}
    \right)^{-1} \bar \lambda_{\bar z} = 0\;.
  \end{multlined}
\end{align}
In this case it is natural to integrate over the Riemann surface using the form \( \di z \wedge \bar \lambda \) and obtain the four-dimensional scalar equations of motion as
\begin{equation}
  \int_\Sigma E \di z \wedge \bar \lambda = \int_\Sigma \bar E \di \bar z \wedge \lambda = 0 \, .
\end{equation}
The details of the calculation are similar to those of the vector equation. The end result is
\begin{align}
  \begin{multlined}[.9\textwidth]
    \left( \tau - \bar \tau \right) \del_\mu \del_\mu a + \del_\mu a \del_\mu \tau +  \frac{\di \bar \tau}{\di \bar a} \wt{\cF}_{\mu\nu} \wt{\cF}_{\mu\nu} \\
    -2 \left( \tau - \bar \tau \right) \hat\omega_{\mu\nu} \cF_{\mu\nu} + 2 \left( L_1 - L_2 \right) \left( \frac{\di \bar a}{\di \bar u} \right)^2 \hat\omega_{\mu\nu} \wt{\cF}_{\mu\nu} = 0 \; ,
  \end{multlined}\\
 \begin{multlined}[.9\textwidth]
   \left( \tau - \bar \tau \right) \del_\mu \del_\mu \bar a - \del_\mu \bar a \del_\mu \bar \tau - \frac{\di \tau}{\di a} \cF_{\mu\nu} \cF_{\mu\nu} \\
- 2 \left( \tau - \bar \tau \right) \hat\omega_{\mu\nu} \wt{\cF}_{\mu\nu} + 2 \left( \bar L_1 - \bar L_2 \right) \left( \frac{\di a}{\di u} \right)^2 \hat\omega_{\mu\nu} \cF_{\mu\nu } = 0\; ,
  \end{multlined}
\end{align}
where \( L_1  \) and \( L_2 \) are the integrals
\begin{align}
  L_1 &= -\int_\Sigma \del\left(\frac{\del s}{1 + \abs{\del s}^2}\right) (\bar s+\bar s - z\bdel\bar s - \bar z\bdel \bar s) \lambda_{\bar z} \di z \wedge   \bar \lambda \, ,\\
  L_2 &= \int_\Sigma \bar \lambda_{\bar z}  \di z \wedge   \bar \lambda \, .
\end{align}
The second integral can be evaluated straightforwardly  in terms of \( u \)  using the methods of Appendix~\ref{sec:line-integrals}:
\begin{equation}
  L_2 = \int_\Sigma \bar \lambda_{\bar z}^2 \di z \wedge \di \bar z  = {\pi \im}
  \left( \frac{ u - 1}{\abs{u - 1}} - \frac{  u + 1}{\abs{u + 1}} \right) \, .
\end{equation}
The evaluation of \( L_1 \) is more involved but leads to $L_1=L_2$ (see the appendix).

The scalar equations take the final form
\begin{align}
  \begin{multlined}[.9\textwidth]
    \label{eq:scalar-equation-a}
    \left( \tau - \bar \tau \right) \del_\mu \del_\mu a + \del_\mu a  \del_\mu \tau + 2 \frac{\di \bar \tau}{\di \bar a} \left( F_{\mu\nu} F_{\mu\nu} + F_{\mu\nu} \dual{F}_{\mu\nu} \right) \\
    + 4 \frac{\di \bar \tau}{\di \bar a} \left( a - \bar a \right) \hat\omega^+_{\mu\nu} F_{\mu \nu} - 4 \left( \tau - \bar \tau \right) \hat\omega^-_{\mu\nu} F_{\mu\nu} = 0\; ,
  \end{multlined}\\
  \begin{multlined}[.9\textwidth]
    \label{eq:scalar-equation-abar}
    \left( \tau - \bar \tau \right) \del_\mu \del_\mu \bar a - \del_\mu \bar a \del_\mu \bar \tau - 2 \frac{\di \tau}{\di a} \left( F_{\mu\nu} F_{\mu\nu} - F_{\mu\nu} \dual{F}_{\mu\nu} \right) \\
    + 4 \frac{\di \tau}{\di a} \left( a - \bar a \right) \hat\omega^-_{\mu\nu} F_{\mu \nu} - 4 \left( \tau - \bar \tau \right) \hat\omega^+_{\mu\nu} F_{\mu\nu} = 0\; .
  \end{multlined}
\end{align}

\paragraph{The four-dimensional action.}

It is well known that the equations of motion for a generic \M5 embedding do not stem from a six-dimensional action. On the other hand our calculation results in the four-dimensional equations of motion for the \( \Omega \)--deformation of the \ac{sw} theory, which we expect to have a Lagrangian description. In fact, a direct calculation shows that the vector equation~\eqref{eq:vector-equation} and the two scalar equations~\eqref{eq:scalar-equation-a} and~\eqref{eq:scalar-equation-abar} are all derived from the variation of the following Lagrangian:
\begin{multline}
   \im \mathscr{L} =- \left( \tau - \bar \tau \right) \left[ \tfrac{1}{2}\del_\mu a \del_\mu \bar a + F_{\mu\nu} F_{\mu\nu} + \left( a - \bar a \right) \dual{\hat\omega}_{\mu\nu} F_{\mu\nu} - 2 \del_\mu \left( a + \bar a \right) \hat\omega_{\mu \nu} A_\nu \right]  \\
  %
  + \left( \tau + \bar \tau \right) \left[ F_{\mu\nu} \dual{F}_{\mu\nu} + \left( a - \bar a \right) \hat\omega_{\mu\nu} F_{\mu\nu} + 2 \del_\mu \left( a - \bar a \right) \hat\omega_{\mu \nu} A_\nu \right] \, .
\end{multline}
This is the main result of this paper and represents the \( \Omega \)--deformation of the \ac{sw} action. In this form the action is not manifestly gauge invariant. An equivalent, gauge invariant, form is given by
\begin{multline}
   \im  \mathscr{L} = - \left( \tau - \bar \tau \right)  \left[ \tfrac{1}{2} \del_\mu a \del_\mu \bar a + F_{\mu\nu} F_{\mu\nu} +  \left( a - \bar a \right) \dual{\hat\omega}_{\mu\nu} F_{\mu\nu} - 2 \del_\mu \left( a + \bar a \right) \dual{F}_{\mu \nu}  \dual{\hat U}_\nu \right] \\
   +  \left( \tau + \bar \tau \right)  \left[ F_{\mu\nu} \dual{F}_{\mu\nu} + \left( a - \bar a \right) \hat\omega_{\mu\nu} F_{\mu\nu} + 2 \del_\mu \left( a - \bar a \right) \dual{F}_{\mu \nu}  \dual{\hat U}_\nu \right] \, ,
\end{multline}
where $\omega = \di U$ and $\dual{\omega} = \di \dual{U}$.

Let us consider some generalizations of our calculation.  It is natural to write the action in a more supersymmetric form as a sum of squares:
\begin{multline}
 \im \mathscr{L} = - \left( \tau - \bar \tau \right) \Big[ \tfrac{1}{2}\left( \del_\mu a + \frac{2 \bar \tau }{\tau - \bar \tau} \dual{F}_{\mu\nu} \dual{\hat U}_\nu \right) \left( \del_\mu \bar a - \frac{2 \tau }{\tau - \bar \tau} \dual{F}_{\mu\nu} \dual{\hat U}_\nu \right) \\
  + \left( F_{\mu\nu} + \tfrac{1}{2} \left( a - \bar a \right) \dual{\hat\omega}_{\mu\nu} \right) \left( F_{\mu\nu} + \tfrac{1}{2} \left( a - \bar a \right) \dual{\hat\omega}_{\mu\nu} \right) \Big] \\
  +  \left( \tau + \bar \tau \right) \left( F_{\mu\nu} + \tfrac{1}{2} \left( a - \bar a \right) \dual{\hat\omega}_{\mu\nu} \right) \left( \dual{F}_{\mu\nu} + \tfrac{1}{2} \left( a - \bar a \right) \hat\omega_{\mu\nu}\right) \; .
\end{multline}
This therefore leads to a prediction for the ${\mathcal O}(\epsilon^2)$ terms. Note however that there could also be additional ${\mathcal O}(\epsilon^2)$ terms which are complete squares on their own, similar to the last term in (\ref{action}).

Finally, although our calculations were only performed in the simplest case of an $SU(2)$ gauge group with one modulus, it is natural to propose that the generalization to arbitrary gauge group and matter content is given by
\begin{multline}
 \im  \mathscr{L} = - \left( \tau_{ij} - \bar \tau_{ij} \right) \Big[ \tfrac{1}{2}\left( \del_\mu a^i + 2\left(\tfrac{  \bar \tau }{\tau - \bar \tau}\right)_{ik} \dual{F}^{k}_{\mu\nu} \dual{\hat U}_\nu \right) \left( \del_\mu \bar a^j -2 \left(\tfrac{  \tau }{\tau - \bar \tau}\right)_{jl} \dual{F}^{l}_{\mu\nu} \dual{\hat U}_\nu \right) \\
  + \left( F^i_{\mu\nu} + \tfrac{1}{2} \left( a^i - \bar a^i \right) \dual{\hat\omega}_{\mu\nu} \right) \left( F^j_{\mu\nu} + \tfrac{1}{2} \left( a^j - \bar a^j \right) \dual{\hat\omega}_{\mu\nu} \right) \Big] \\
+ \left( \tau_{ij} + \bar \tau_{ij} \right) \left( F^i_{\mu\nu} + \tfrac{1}{2} \left( a^i - \bar a^i \right) \dual{\hat\omega}_{\mu\nu} \right) \left( \dual{F}^{j}_{\mu\nu} + \tfrac{1}{2} \left( a^j - \bar a^j \right) \hat\omega_{\mu\nu}  \right)\ ,
\end{multline}
where we have used a suitable form for the inverse of $(\tau - \bar\tau)_{ij}$ which is taken to act from the left.

\section{Conclusions}\label{sec:conclusions}

In this paper we have computed the corrections to first order in $\epsilon$ to an \M5--brane wrapping a Riemann surface in the $\Omega$--background of~\cite{Hellerman:2011mv,Reffert:2011dp,Hellerman:2012zf}. The result can be viewed as the leading correction to the Seiberg--Witten effective action of $\mathcal{N}=2$ super-Yang--Mills theory with an $\Omega$--deformation.

The corrected effective action includes a shift in the gauge field strength as well as a sort of generalized covariant derivative for the scalar, including a non-minimal coupling to the gauge field.  A similar generalized covariant derivative  already appears in (\ref{action}) and is reminiscent of the equivariant differential used in~\cite{Nekrasov:2002qd}.

It is important to ask why the result we obtain, calculated as the classical motion of a single \M5--brane in M--theory, can capture quantum effects in four-dimensional gauge theory. To answer this we should restore the factors of $R$ and $\Lambda$ into the Riemann surface. This can be achieved by simply rescaling $\del s\to \Lambda^2 R\del s$, $\del s / \del a\to R  \del s / \del a$ and $\del s / \del u\to R  \del s / \del u$ along with their complex conjugates. However this replacement does not affect the final equations. On the other hand $R=g_sl_s$ can be related to the gauge coupling constant $g_4$ in the string theory picture. Thus the classical M--theory calculation in fact captures all orders of the four-dimensional gauge theory.

\section*{Acknowledgments}

We would like to thank Paul Howe for helpful correspondence.

redpajama_set_name: RedPajamaArXiv


text:
Posts Tagged 'Woman's Hour'
On the Thursdays with no new AMT, we crank up the spoken word audio and have a Thursday Listening Party.
In the early days of AMT (episode 16!) a listener called Benjamin Partridge posed the question, "Is Bremen in Germany a weird place to want to go on holiday?" He found out the answer for himself in episode 20. In the intervening years, I've met Bremenjamin Partridge in real life, and now I learn he has started a funny new podcast, The Beef and Dairy Network, which will be your kind of thing if you enjoy Down the Line or Chris Morris's early-career gadding about. Or beef and dairy.
True crime time: there's a new podcast, Detective, in which a retired lieutenant recounts stories from his 23 years in the Homicide Division. Give it a whirl if you like hearing about police procedure and don't mind some gore.
I've been enjoying Late Night Woman's Hour, hosted by Lauren Laverne, and thought the episode discussing masculinity was particularly interesting, even if I did want to shout "Shut up!" at the radio whenever one of the speakers was talking. I'll leave you to guess which one. (Not super-podcaster Richard Herring.)
Do you like The Moth or Mortified or Spark London or other shows where people get on stage and tell stories from their lives? I just hosted a pilot of one such show, Truth Be Told, and if you like it, do tweet and email BBC Radio 4 demanding a full series.
Tomorrow, there'll be a new episodes of: i) The Media Podcast featuring Olly up at the Edinburgh Festival; ii) The Allusionist, featuring me sliding off my chair after staring at an edit screen for 16-hour days on end. Meanwhile, catch up on the most recent episode about word games (and Jenga!) at theallusionist.org/word-play.
Which is more agonising: having to help your parents with their computer, or being faced with your parents' sex lives? Answer: BOTH AT ONCE, as suffered by a questioneer in AMT321. Hear their pain, and join us for a fresh dose of other people's pain next Thursday.
What's in your ears, dears?
Recommend shows in the comments.
Tags:BBC Radio 4, Benjamin Partridge, Detective, The Beef and Dairy Network, Thursday Listening Party, Truth Be Told, Woman's Hour
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What have you been listening to this week? Here's what I have been feeding my ears:
Cheese fans, chew on this episode of Gastropod, which is a very interesting tour through the history and science of cheese (a rather more thorough one than ours). Cheese begat written language! What a magnificent substance it is.
Similarly detailed is Song Exploder, on which musicians dissect their own songs to show how they were composed and produced. It's fascinating stuff. I was particularly tickled by the National's tale of harmonica versus a perforated eardrum.
In Out of Date, each week Dave Cribb and Pete Allison go on dates then do post-match analysis. Is it wrong that I kind of hope they don't find love so they have to keep making the show? (Of course it is wrong. I know that. Shut up.)
What we've been up to:
You can hear Olly on his new LBC show 8-10pm Fridays and 6.30-10pm Saturdays, and on The Media Podcast, a new episode of which will appear by the end of this week.
On Monday, I was on Woman's Hour's craft special, teaching Jane Garvey how to make a kimono out of charity shop scarves. She took to sewing like a duck to snooker. A triumph! Anyway, if you want to make your own and the audio is not a fully instructive tutorial, click here. It's a lot easier than it sounds.
In the new Allusionist, I spoke to crossword-setter (and AMT listener!) John Feetenby about how he creates those dastardly cryptic clues. He even managed to come up with one for 'Zaltzman'! That's a career high. Visit theallusionist.org/crosswords for more.
In AMT311, we discussed the Starbucks logo, the Hollywood Walk of Fame, and avoiding being eaten by rats while you're having sex. Catch up, then return next Thursday for AMT312.
Tags:BBC, crosswords, Gastropod, Jane Garvey, Out of Date, podcasts, Radio 4, Song Exploder, Thursday Listening Party, Woman's Hour
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Noises from home:
Exciting news: Martin's got a new album coming out on Saturday! Go here to preview three of the tracks and to buy; it's £5 to preorder but pay what you want when it is released. Or, if you are a retronaut who prefers your music on a physical format, wait a couple more weeks and then buy one of the forthcoming limited-edition CDs with a handmade papercut sleeve (if you follow Martin on Instagram, you may have seen some sneak peeks).
There's a new news-themed episode of the Sound Women podcast, in which Olly's LBC colleague Petrie Hosken tells me how she felt safer nearly getting kidnapped as a war correspondent in Bosnia than as a woman working in British radio. Good times!
Apparently there's been some Royal News this week? [Shrug] It's an ongoing mystery at AMT that none of us give a shit about the royal family, and yet questions about them are always fruitful on the podcast. So whether you give shits or not, have a go on the Answer Me This! Jubilee album for an hour of regal hijinks.
Noises from elsewhere:
The show Strangers is always worth your time, but particularly the recent Love Hurts episodes (part 1 and part 2), in which Lea Thau transforms the question 'Why are you single?' from an awful thing Smug Marrieds say to a very personal and reflective investigation into why she has been reluctantly single for the past four years. At least, judging by the exes who appear on the show, she's dated some Good Sports during that time…
From Strangers to friends: I really enjoyed this Woman's Hour/Men's Hour collaboration all about friendship. Of course, they cover the When Harry Met Sally adage that men and women can't be friends, which Olly and I have been disproving throughout our fourteen-year friendship. If you need additional on-air partnerships as evidence, I direct you to the programme's guest Geoff Lloyd, whose brilliant Hometime Show on Absolute Radio with Annabel Port crackles with sexless tension.
Various AMT friends have been busy piping up this week. Ruth Barnes from Amazing Radio made a terrific Radio 4 documentary about folk singer Judee Sill, who had a beautiful voice and a tragic mess of a short life.
And finally: I was thrilled to hear two AMTpals and primo podcasters team up, when Little Atoms' Neil Denny went on Dave Pickering's Getting Better Acquainted. They talk about reading books, prayer, and masturbation – all the solitary entertainments, really.
I'm always listening out for shows to try; please recommend some in the comments.
PS In case you missed it: my Bugling brother Andy and I were interviewed by the Guardian about why the Zaltzman family communicates in jokes rather than human emotions. Click here to read it.
Tune in to our various other gigs:
• Catch up on AMT297 and the episodes preceding it.
• AMT episodes 1-170 and the special AMT albums are all available for a piddling little price at answermethisstore.com, and if you buy any of them you're bankrolling the podcast, for which we are extremely grateful.
• Olly's on LBC every weekday 1am-4am. Set your alarm.
• I host the monthly Sound Women podcast and am on Let's Talk About Tech from BBC 5 Live.
• Martin the Sound Man makes numerous other podcasts, including Brain Train, The Global Lab and The Sound of the Ladies.
Tags:Annabel Port, BBC, dating, Dave Pickering, Friends, friendship, Geoff Lloyd, Getting Better Acquainted, Judee Sill, Lea Thau, Little Atoms, love, Martin Austwick, Men's Hour, music, Neil Denny, Petrie Hosken, Radio 4, Sound Women, strangers, When Harry Met Sally, Woman's Hour
YOU ARE CORDIALLY INVITED TO ALL PREVIOUS
THURSDAY LISTENING PARTIES.
CLICK HERE TO ATTEND.
B.Y.O.B. AND HEADPHONES
In case you're interested in podcasters talking shop, we've started putting up the full-length interviews we conducted for our podcasting documentary on Radio 4. My thoughts on talking to Maron, Savage, Mars etc al (and my brother) are here.
Long-term AMT listeners will already be familiar with my thoughts upon My So-Called Life, but I aired them at greater length on Little Atoms. You're very welcome.
Then, in the May edition of the Sound Women podcast, I reflect upon My Brilliant Career coughspluttercough, and also learn about prison radio, headed notepaper campaigns, and how YouTube stars are made (talking about hair, apparently):
Further audiotainment:
I've spent much of this week doing a large and very fiddly drawing with a tiny dip pen last used by my grandfather at school. My eyes were busy, but my ears were not, so it was an optimal time redress how lately I've been slacking on This American Life-listening duties – so many other shows are influenced by This American Life, it made me take the actual This American Life for granted. But blasting through several episodes, including this week's Call for Help, brought me right back in. I'll never leave you again, This American Life!
I chased this with an episode of TLDR featuring Alex Tew, who in 2005 created the Million Dollar Homepage whilst sitting around waiting to go to university. Nowadays the site is a bit of a joke for being a relic of a past internet age, and for being more than 20% dead links – but to me, it's incredible that it is still nearly 80% undead, and still hauling in money. While I was waiting to go to university, I learnt Italian, which earnt me zero dollars and I've since forgotten nearly 100% of it. You win this round, Alex Tew!
Drawing with a dip pen takes a REALLY long time, so I also blasted through two series of Radio 4's The Ideas That Make Us, which is the kind of radio show that makes you feel cleverer as you listen (like In Our Time) whilst being very fun (unlike In Our Time). (Sorry, In Our Time. Melvyn Bragg, please don't enact revenge on Bettany Hughes for my offence.)
Recently Woman's Hour ran a belter of a fashion special, featuring such legends as Celia Birtwell, and Grayson and Philippa Perry; there was the serious business of sustainable clothing and the Rana Plaza disaster, and the less serious business of stripes and how they used to be the pattern of the devil. The more you know, eh?
Lastly, if you're interested in how writing for TV goes:
Greg Jenner, historical consultant for Horrible Histories, discusses writing historical documentaries and dramas.
Brent Forrester, who has worked on such shows as The Simpsons, King of the Hill, Mr Show and the American version of The Office, talks about the sweaty business of comedy writing.
Housekeeping:
• AMT episodes 1-170 and the special AMT albums are all available for a piddling little price at answermethisstore.com, and if you buy any of them you're bankrolling the podcast, so thank you very much indeed.
• Olly's on LBC every weekday 1am-4am. If you're an insomniac, a night worker, or in a time zone where those hours are compatible with waking life, tune in.
• On Saturday evenings I'm on BBC 5 Live's Saturday Edition, available subsequently as the podcast Let's Talk About Tech.
• I also host the monthly Sound Women podcast.
To keep your ears ever busy until AMT290 next Thursday, here are some other podcasts we like.
Requests are welcome at the Thursday Listening Party. No need to dance sexily next to the DJ booth hoping to be noticed, just recommend shows in the comments.
Tags:Alex Tew, Bettany Hughes, Ira Glass, Little Atoms, Million Dollar Homepage, MSCL, My So-Called Life, On the Media, Sound Women, TAL, This American Life, Thursday Listening Party, TLDR, Woman's Hour
EPISODE 135 – peace babies
Hello little chums,
It's all very unsettling, this regime change and Conservacrat coalitions and so on; so let's stick with things that are comforting and familiar. Corduroy, say, or those sweetie prawns you only get as part of pick'n'mix, or the face of Richard Madeley. All that and more things which aren't the sour tang of political discomfort in Answer Me This! Episode 135:
Within we speak of:
the Dyson fan
onion cocaine
irresponsible science teachers
concentrated pigments
Mike Patton's travel wash
Common's dry hands
Daphne and Celeste
survival vs. the Red Hot Chili Peppers
FishMac
the Whigs
Gideon Sundback
the mischief of tailors
Hot Pittites.
Plus: Olly hates jelly babies despite their brilliant capacity for mischief; Helen finds an unlikely way for widowers to assuage their grief; and Martin the Sound Man violates Olly at the Sony Awards. Cheeky chappie. You can see and hear him being much better behaved on this educational video and the Bright Club podcast.
Since this is an interactive podcast, please interact with us by asking your QUESTIONS: do that with your voices, by leaving a message on 0208 123 5877 or Skype ID answermethis; or do that with your words by emailing them to answermethispodcast@googlemail.com.
See you next Thursday!
Helen and Olly
• App • Facebook • Twitter • Merch Superstore • YouTube Channel •
Tags:Apple, bad manners, celebrities, childhood, condiments, confectionery, Conservatives, corduroy, election, fans, fashion, festivals, First World War, fish, five a day, food, green, history, hygiene, inventions, James Dyson, jelly babies, Jenni Murray, Katie Melua, lessons, Mac, McDonald's, myths, piss, Radio 4, Richard Madely, rock, royalty, salad cream, school, Sony Awards, Steve Jobs, stupid, stupid campaigns, suits, Tories, vegetarianism, war, William Pitt the Younger, Woman's Hour, yuk, zips

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October 21, 2020 All About Wheels - Automotive (Cars / All About Wheels - Automotive (Cars, Car Clubs, SUV's, RV's etc) / Lifestyle features / Press releases
Nissan unveils enhancements to the iconic Nissan Patrol Super Safari with its 2021 edition
With new exterior colours, redesigned rims and advanced connectivity, the design uplift will be sure to impress fans of the legendary vehicle
Nissan announces the arrival of the 2021 Nissan Patrol Super Safari to the Middle East, featuring a range of design and tech enhancements to the iconic off-road vehicle. With three new colour combinations, alloy wheels and other striking exterior and interior upgrades, the 2021 model brings a fresh look to its exceptional performance and enduring legacy as one of the most coveted SUVs in the region.
The 2021 Super Safari will be available in a black exterior colour, adding to the existing white and gold body colours. Drivers can also select a new gold accent across the roof, bumpers and spare tyre cover as an alternative to the dual tone accent from previous models, to create the combination of their choice. Furthermore, the new model will sport a refreshed graphic for the classic 'Super Safari' decal along the side of the car.
Complementing the exterior upgrades are the new 17-inch alloy wheels, with a diamond cut and black paint for a more refined look.
The interiors of the 2021 Super Safari also feature an uplift, with new tan leather and cloth options to seat you comfortably. A special Super Safari embossing also adds a unique touch to the tan leather seat options.
Drivers can also focus on enjoying their driving experience with a new 8" display and audio system with Apple Carplay which provides seamless integration to contacts, preferred audio apps and more.
Thierry Sabbagh, Managing Director, Nissan Middle East said: "The region's sustained love and demand for the Patrol Super Safari is reflective of the deep-rooted heritage of this all-terrain vehicle with the deserts of the Arabian Peninsula. The 2021 edition adds a modern look to the powerful performance and durability of the SUV – maintaining its credibility to be the ideal partner for off-road driving adventure across the region."
The 2021 Nissan Patrol Super Safari is now available at showrooms across the region, at a starting price of AED 171,000 with VAT (US $47,000). Prices per country will vary from market to market.
For more information on the 2021 Nissan Patrol Super Safari, please contact your nearest authorized Nissan dealership, or visit: https://www.nissan-me.com/
For more information about our products, services and commitment to sustainable mobility, visit Nissan AMI. You can follow us on Facebook, Instagram, Twitter and LinkedIn and see all our latest videos on YouTube.
Jaguar land rover using aerospace technology to develop future lightweight vehicles


My book-in-progress "Who Built the Earth?" is an exploration of scientific evidence in support of the Artificial Earth Hypothesis, which suggests that the earth was constructed by an advanced race or races in the distant past. The book's estimated completion date is October 2020. Chapter titles are below.
Author, Who Built the Earth?
Was Earth Formed by Natural Gravitational Accretion?
How Might the Earth Have Been Built?
Are All Planets and Moons in the Solar System Artificial?
Is Earth a Tourist Destination?
10. Who Is Building the Earth Today?
Are the Planet Builders Still Here?