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Add branes at angles

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Signed-off-by: Riccardo Finotello <riccardo.finotello@gmail.com>
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Riccardo
2020-11-05 23:46:30 +01:00
parent ae81499544
commit 1c316a7ab1
2 changed files with 80 additions and 13 deletions
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58
thesis.tex
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@@ -117,15 +117,15 @@
\end{center}
}
\setbeamertemplate{footline}{%
\usebeamerfont{footnote}
\usebeamercolor{footnote}
\hfill
\insertframenumber{}~/~\inserttotalframenumber{}
\hspace{1em}
\vspace{1em}
\par
}
% \setbeamertemplate{footline}{%
% \usebeamerfont{footnote}
% \usebeamercolor{footnote}
% \hfill
% \insertframenumber{}~/~\inserttotalframenumber{}
% \hspace{1em}
% \vspace{1em}
% \par
% }
% \AtBeginSection[]
% {%
@@ -157,7 +157,7 @@
}
{%
\setbeamertemplate{footline}{}
% \setbeamertemplate{footline}{}
\usebackgroundtemplate{%
\transparent{0.1}
\includegraphics[width=\paperwidth]{img/torino.png}
@@ -331,13 +331,16 @@
\item $N = 1$ \textbf{supersymmetry} is preserved in 4D
\item algebra of $\mathrm{SU}(3) \otimes \mathrm{SU}(2) \otimes \mathrm{U}(1)$ contained in arising \textbf{gauge group}
\item algebra of $\mathrm{SU}(3) \otimes \mathrm{SU}(2) \otimes \mathrm{U}(1)$ in arising \textbf{gauge group}
\end{itemize}
\end{column}
\begin{tikzpicture}[remember picture, overlay]
\node[anchor=base] at (3em,-3.75em) {\includegraphics[width=0.3\linewidth]{img/cy}};
\end{tikzpicture}
\begin{column}{0.3\linewidth}
\centering
\includegraphics[width=0.9\columnwidth]{img/cy}
% \centering
% \includegraphics[width=0.9\columnwidth]{img/cy}
\end{column}
\end{columns}
\end{block}
@@ -478,8 +481,37 @@
\begin{equationblock}{Twist Fields Correlators}
\begin{equation*}
\left\langle \prod\limits_{t = 1}^N \upsigma_{\mathrm{M}_{(t)}}\qty( x_{(t)} ) \right\rangle
=
\mathcal{N}\qty( \qty{ x_{(t)},\, \mathrm{M}_{(t)} }_{1 \le t \le N_B} )
e^{- S_{E\, (\text{cl})}\qty( \qty{ x_{(t)},\, \mathrm{M}_{(t)} }_{1 \le t \le N_B} )}
\end{equation*}
\end{equationblock}
\pause
\begin{tikzpicture}[remember picture, overlay]
\draw[line width=4pt, red] (29.5em,3.5em) ellipse (2cm and 1cm);
\end{tikzpicture}
\pause
\begin{columns}
\begin{column}{0.5\linewidth}
\centering
\resizebox{0.5\columnwidth}{!}{\import{img}{branesangles.pgf}}
\end{column}
\begin{column}{0.5\linewidth}
D-branes in \textbf{factorised} internal space:
\begin{itemize}
\item \textbf{embedded as lines} in $\mathds{R}^2 \times \mathds{R}^2 \times \mathds{R}^2$
\item \textbf{relative rotations} are $\mathrm{SO}(2) \simeq \mathrm{U}(1)$ elements
\item $S_{E\, (\text{cl})}\qty( \qty{ x_{(t)},\, \mathrm{M}_{(t)} }_{1 \le t \le N_B} ) \sim \text{Area}\qty( \qty{ f_{(t)},\, \mathrm{R}_{(t)} }_{1 \le t \le N_B} )$
\end{itemize}
\end{column}
\end{columns}
\end{frame}
\section[Time Divergences]{Cosmological Backgrounds and Divergences}