Add up to intersecting branes

Signed-off-by: Riccardo Finotello <riccardo.finotello@gmail.com>

img/chanpaton.pgf

@@ -7,16 +7,16 @@
 
 % draw strings
 \draw[decorate, decoration={snake, segment length=1cm}, dash pattern=on 2.45cm off 1pt on 1pt off 1pt on 1pt off 1pt on 1pt off 1pt on 1pt off 1pt on 1pt off 1pt on 1pt off 1pt on 1pt off 1pt on 1pt off 1pt, postaction={decoration={markings, mark=at position 0.5 with {\arrow{>}}}, decorate}] (0.5cm, 3cm) -- (3cm, 1.5cm);
-\node[anchor=base] (l1) at (1.75cm, 2.75cm) {$\tensor{\lambda}{^1_1_2}$};
+\node[anchor=base] (l1) at (1.75cm, 2.75cm) {$\tensor{\uplambda}{^1_1_2}$};
 
 \draw[decorate, decoration={snake, segment length=1cm}, dash pattern=on 2.45cm off 1pt on 1pt off 1pt on 1pt off 1pt on 1pt off 1pt on 1pt off 1pt on 1pt off 1pt on 1pt off 1pt on 1pt off 1pt on 1pt off 1pt, postaction={decoration={markings, mark=at position 0.5 with {\arrow{>}}}, decorate}] (3cm, 3cm) -- (5.5cm, 1.5cm);
-\node[anchor=base] (l2) at (4.25cm, 2.75cm) {$\tensor{\lambda}{^2_2_3}$};
+\node[anchor=base] (l2) at (4.25cm, 2.75cm) {$\tensor{\uplambda}{^2_2_3}$};
 
 \draw[decorate, decoration={snake, segment length=1cm}, postaction={decoration={markings, mark=at position 0.765 with {\arrow{>}}}, decorate}] (3cm, 2.5cm) .. controls (3.5cm, 2cm) and (3.5cm, 1cm) .. (3cm, 0.5cm);
-\node[anchor=base] (l3) at (4cm, 1.5cm) {$\tensor{\lambda}{^3_2_2}$};
+\node[anchor=base] (l3) at (4cm, 1.5cm) {$\tensor{\uplambda}{^3_2_2}$};
 
 \draw[decorate, decoration={snake, segment length=1cm}, dash pattern=on 5.15cm off 1pt on 1pt off 1pt on 1pt off 1pt on 1pt off 1pt on 1pt off 1pt on 1pt off 1pt on 1pt off 1pt on 1pt off 1pt on 1pt off 1pt on 1pt off 1pt, postaction={decoration={markings, mark=at position 0.5 with {\arrow{<}}}, decorate}] (0.5cm, 1cm) .. controls (1.5cm, 0cm) and (4cm, 0cm) .. (5.5cm, 1cm);
-\node[anchor=base] (l4) at (3cm, -0.5cm) {$\tensor{\lambda}{^4_3_1}$};
+\node[anchor=base] (l4) at (3cm, -0.5cm) {$\tensor{\uplambda}{^4_3_1}$};
 
 \end{tikzpicture}
 

img/smbranes.pgf

@@ -0,0 +1,31 @@
+\begin{tikzpicture}
+
+% draw the baryonic stack
+\draw[thick] (-2.5cm, 5cm) -- (2.5cm, 5cm);
+\draw[thick] (-2.5cm, 4.9cm) -- (2.5cm, 4.9cm) node[anchor=west] (baryonic) {baryonic $\qty(Y = \frac{1}{3} )$};
+\draw[thick] (-2.5cm, 4.8cm) -- (2.5cm, 4.8cm);
+
+% draw the left stack
+\draw[thick] (-2.25cm, 5.25cm) -- (-2.25cm, 0cm);
+\draw[thick] (-2.15cm, 5.25cm) -- (-2.15cm, 0cm) node[anchor=north east] (left) {left $\qty( Y = - \frac{1}{2} )$};
+
+% draw leptonic and right stacks
+\draw[thick] (-2.5cm, 2.5cm) -- (2.5cm, 2.5cm) node[anchor=west] (l1) {leptonic $\qty( Y = 0 )$};
+\draw[thick] (-2.5cm, 0.5cm) -- (2.5cm, 0.5cm) node[anchor=west] (l2) {leptonic $\qty( Y = -1 )$};
+\draw[thick] (0cm, 5.25cm) -- (0cm, 0cm) node[anchor=north] (r1) {right $\qty( Y = -1 )$};
+\draw[thick] (2.25cm, 5.25cm) -- (2.25cm, 0cm) node[anchor=north west] (r2) {right $\qty( Y = 0 )$};
+
+% draw left quarks
+\draw[decorate, decoration={snake, segment length=0.5cm}, postaction={decoration={markings, mark=at position 0.5 with {\arrow{>}}}, decorate}] (-2.15cm, 3.5cm) node[anchor=south east] {$\mqty( u_L \\ d_L )$} -- (-1cm, 4.8cm);
+% draw up right quark
+\draw[decorate, decoration={snake, segment length=0.5cm}, postaction={decoration={markings, mark=at position 0.5 with {\arrow{<}}}, decorate}] (0cm, 3.5cm) node[anchor=east] {$\overline{u}_R$} -- (1cm, 4.8cm);
+% draw down right quark
+\draw[decorate, decoration={snake, segment length=0.5cm}, postaction={decoration={markings, mark=at position 0.5 with {\arrow{<}}}, decorate}] (2.25cm, 3.5cm) node[anchor=west] {$\overline{d}_R$} -- (1.15cm, 4.8cm);
+% draw left leptons
+\draw[decorate, decoration={snake, segment length=0.5cm}, postaction={decoration={markings, mark=at position 0.5 with {\arrow{>}}}, decorate}] (-2.15cm, 0.9cm) node[anchor=south east] {$\mqty( \upnu^e_L \\ e^-_L )$} -- (-1cm, 2.5cm);
+% draw right leptons
+\draw[decorate, decoration={snake, segment length=0.5cm}, postaction={decoration={markings, mark=at position 0.5 with {\arrow{<}}}, decorate}] (0cm, 0.9cm) node[anchor=east] {$\overline{e}^+_R$} -- (1cm, 2.5cm);
+
+\end{tikzpicture}
+
+% vim: ft=tex

thesis.tex

@@ -48,7 +48,7 @@
 
 \newenvironment{equationblock}[1]{%
   \begin{block}{#1}
-  \vspace*{-\baselineskip}\setlength\belowdisplayshortskip{0pt}
+  \vspace*{-0.75\baselineskip}\setlength\belowdisplayshortskip{0.25\baselineskip}
 }{%
   \end{block}
 }
@@ -131,6 +131,11 @@
 % {%
 %   {%
 %     \setbeamertemplate{footline}{}
+%     \usebackgroundtemplate{%
+%       \transparent{0.1}
+%       \includegraphics[width=\paperwidth]{img/torino.png}
+%     }
+%     \addtobeamertemplate{background canvas}{\transfade[duration=0.25]}{}
 %     \begin{frame}[noframenumbering]{\contentsname}
 %       \tableofcontents[currentsection]
 %     \end{frame}
@@ -315,7 +320,7 @@
   \begin{frame}{Extra Dimensions and Compactification}
     \begin{block}{Compactification}
       \begin{columns}
-        \begin{column}{0.6\linewidth}
+        \begin{column}{0.7\linewidth}
           \begin{equation*}
             \mathscr{M}^{1,\, 9}
             =
@@ -330,9 +335,9 @@
           \end{itemize}
         \end{column}
 
-        \begin{column}{0.4\linewidth}
+        \begin{column}{0.3\linewidth}
           \centering
-          \includegraphics[width=0.7\columnwidth]{img/cy}
+          \includegraphics[width=0.9\columnwidth]{img/cy}
         \end{column}
       \end{columns}
     \end{block}
@@ -372,7 +377,7 @@
 
     \pause
 
-    \begin{block}{T-duality}
+    \begin{equationblock}{T-duality}
       \begin{equation*}
         X( z, \overline{z} )
         =
@@ -386,7 +391,7 @@
         =
         Y( z ) + \overline{Y}( \overline{z} )
       \end{equation*}
-    \end{block}
+    \end{equationblock}
 
     \pause
 
@@ -408,8 +413,7 @@
 
     \pause
 
-    \begin{block}{Spectrum}
+    \begin{equationblock}{Massless Spectrum (\emph{irrep} of \textbf{little group} $\mathrm{SO}( D - 2 )$}
-      At massless level (\emph{irrep} of \textbf{little group} $\mathrm{SO}( D - 2 )$):
       \begin{equation*}
         \mathcal{A}^{\upmu}
         \quad \leftrightarrow \quad
@@ -435,7 +439,7 @@
           $a = 1,\, 2,\, \dots,\, D - p - 1$
         \end{tabular}
       \end{equation*}
-    \end{block}
+    \end{equationblock}
 
     \pause
 
@@ -457,10 +461,27 @@
         \pause
         \highlight{Build gauge bosons, fermions and scalars.}
       \end{column}
-
     \end{columns}
   \end{frame}
 
+  \begin{frame}{Standard Model-like Scenarios}
+    \centering
+    \resizebox{0.8\linewidth}{!}{\import{img}{smbranes.pgf}}
+  \end{frame}
+
+
+  \subsection[D-branes at Angles]{D-branes Intersecting at Angles}
+
+  \begin{frame}{Intersecting D-branes}
+    Consider \highlight{$N$ intersecting $D6$-branes} filling $\mathscr{M}^{1,3}$ and \textbf{embedded in} $\mathds{R}^6$
+
+    \begin{equationblock}{Twist Fields Correlators}
+      \begin{equation*}
+        \left\langle \prod\limits_{t = 1}^N \upsigma_{\mathrm{M}_{(t)}}\qty( x_{(t)} ) \right\rangle
+      \end{equation*}
+    \end{equationblock}
+  \end{frame}
+
   \section[Time Divergences]{Cosmological Backgrounds and Divergences}
 
   \begin{frame}{BBB}