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Update poster & bump version
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bryango committed Aug 30, 2023
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11 changes: 6 additions & 5 deletions alpha/GlueonAdS/glueon-poster-v2.tex
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Expand Up @@ -250,8 +250,9 @@ \section*{\textbf{Proposal:}\texstringonly{\\}Glue-on $\mrm{AdS}_3$ -- beyond th
\end{equation*}}
\begin{center}
\vspace{-1\baselineskip}%

\centering
\includegraphics[width=.7\linewidth]{img/diagram.pdf}
\includegraphics[width=.8\linewidth]{img/diagram.png}

\vspace{-.45\baselineskip}
\scriptsize\ Top-down view of a constant $t$ slice
Expand Down Expand Up @@ -331,7 +332,7 @@ \section*{\textbf{Proposal:}\texstringonly{\\}Glue-on $\mrm{AdS}_3$ -- beyond th
\end{align}
$\leadsto$ correct charges, the modified signal propagation speed $v'_{\pm} \equiv \pm {d\varphi'}/{dt'}$, and \TTbar \textbf{thermodynamics} upon Wick rotation. In particular,
\begin{equation*}
\hspace{-.5em} \mu > 0,\ \ \,
\hspace{-.8em} \mu > 0,\ \ \,
T_L(\mu)\,T_R(\mu) \le - \frac{1}{4\pi^2 \ell^2 \zeta_c} = \frac{3}{4\pi^2c\mu} = T_H(\mu)^2.
\end{equation*}
$T_{L,R}$: temperatures associated with $u',v' = \varphi' \pm t'$.\\
Expand Down Expand Up @@ -371,8 +372,8 @@ \subsection*{\TTbar partition functions from the bulk} \label{se:partitionfuncti

\item \textbf{Torus:} {modular invariance} \& sparseness of the ``light'' spectrum at large $c$ $\leadsto$ universal form:
\begin{equation*}\small
\hspace{-2.3em}
\log Z_{T\bar T}(\mu) \approx \left\{ \begin{aligned}
\hspace{-2.8em}
\log Z_{T\bar T}(\mu) \approx \left\{ \begin{aligned}
& {-\frac{1}{2}}\,(\beta_L + \beta_R)\, RE_{\text{vac}}(\mu), &\beta_L \beta_R > 1, \\
& {-2 \pi^2 \bigg(\frac{1}{\beta_L} + \frac{1}{\beta_R}\bigg) RE_{\text{vac}}\bigg(\frac{4\pi^2}{\beta_L \beta_R} \mu \bigg)}, &\beta_L\beta_R < 1. %\\[2ex]
\end{aligned} \right. %\label{ZTTbar}
Expand Down Expand Up @@ -402,7 +403,7 @@ \subsection*{\TTbar partition functions from the bulk} \label{se:partitionfuncti
$} and the flow equation \eqref{TTbardef}
admit the general \mbox{solution} with a $\mu$-\textit{independent} integration constant $a$:
\begin{equation*}\small
\hspace{-1.6em}
\hspace{-1.8em}
\log Z_{\TTbar}(\mu, a) = \tfrac{c}{3} \log \Big[\tfrac{R}{a} \Big(1+\sqrt{1-\tfrac{c \mu }{3 R^2}}\, \Big) \Big] - \tfrac{R^2}{\mu} \sqrt{1-\tfrac{c \mu }{3 R^2}} + \tfrac{R^2}{\mu}. %\label{Zsol}
\end{equation*}
\begin{itemize}%[noitemsep]
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