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Add new figures in Tikz

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Signed-off-by: Riccardo Finotello <riccardo.finotello@gmail.com>
This commit is contained in:
Riccardo
2020-10-16 19:01:42 +02:00
parent 366d00ec60
commit 06e27a3702
44 changed files with 823 additions and 727 deletions
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64
sec/part1/dbranes.tex
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@@ -381,8 +381,7 @@ We thus translated the rotations of the D-branes encoded in the matrices $R_{(t)
\begin{figure}[tbp]
\centering
\def\svgwidth{0.5\textwidth}
\import{img}{branchcuts.pdf_tex}
\import{tikz}{branchcuts.pgf}
\caption{%
Branch cut structure of the complex plane with $N_B = 4$.
Cuts are pictured as solid coloured blocks running from one intersection point to another at finite.
@@ -599,8 +598,7 @@ We choose $\bart = 1$ in what follows.
\begin{figure}[tbp]
\centering
\def\svgwidth{0.35\linewidth}
\import{img}{threebranes_plane.pdf_tex}
\import{tikz}{threebranes_plane.pgf}
\caption{%
Fixing the \SL{2}{\R} invariance for $N_B = 3$ and $\bart = 1$ leads to a cut structure with all the cuts defined on the real axis towards $\omega_{\bart} = \infty$.}
\label{fig:hypergeometric_cuts}
@@ -2111,23 +2109,41 @@ Here we compute the parameter $\vec{n}_{1}$ given two Abelian rotation in $\omeg
Results are shown in~\Cref{tab:Abelian_composition}.
\begin{figure}[tbp]
\centering
\begin{subfigure}[b]{0.45\linewidth}
\centering
\def\svgwidth{0.8\textwidth}
\import{img}{abelian_angles_case1.pdf_tex}
\caption{%
The Abelian limit when the triangle has all acute angles.
This corresponds to the cases $n_{0} + n_{\infty}< \frac{1}{2}$ and $n_{0}< n_{\infty}$ which are exchanged under the parity $P_2$.}
\label{fig:Abelian_angles_1}
\import{tikz}{abelian_angles_case1_a.pgf}
\caption{Case 1.}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.45\linewidth}
\centering
\import{tikz}{abelian_angles_case1_b.pgf}
\caption{Case 2.}
\end{subfigure}
\caption{%
The Abelian limit when the triangle has all acute angles.
This corresponds to the cases $n_{0} + n_{\infty}< \frac{1}{2}$ and $n_{0}< n_{\infty}$ which are exchanged under the parity $P_2$.}
\label{fig:Abelian_angles_1}
\end{figure}
\begin{figure}[tbp]
\centering
\begin{subfigure}[b]{0.45\linewidth}
\centering
\def\svgwidth{0.8\textwidth}
\import{img}{abelian_angles_case2.pdf_tex}
\caption{%
The Abelian limit when the triangle has one obtuse angle.
This corresponds to the cases $n_{0} + n_{\infty}> \frac{1}{2}$ and $n_{0}> n_{\infty}$ which are exchanged under the parity $P_2$.}
\label{fig:Abelian_angles_2}
\import{tikz}{abelian_angles_case2_a.pgf}
\caption{Case 1.}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.45\linewidth}
\centering
\import{tikz}{abelian_angles_case2_b.pgf}
\caption{Case 2.}
\end{subfigure}
\caption{%
The Abelian limit when the triangle has one obtuse angle.
This corresponds to the cases $n_{0} + n_{\infty}> \frac{1}{2}$ and $n_{0}> n_{\infty}$ which are exchanged under the parity $P_2$.}
\label{fig:Abelian_angles_2}
\end{figure}
Under the parity transformation $P_2$ the previous four cases are grouped
@@ -2151,8 +2167,17 @@ when all $m = 0$.
\begin{figure}[tbp]
\centering
\def\svgwidth{0.8\textwidth}
\import{img}{usual_abelian_angles.pdf_tex}
\begin{subfigure}[b]{0.45\linewidth}
\centering
\import{tikz}{usual_abelian_angles_a.pgf}
\caption{Case 1.}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.45\linewidth}
\centering
\import{tikz}{usual_abelian_angles_b.pgf}
\caption{Case 2.}
\end{subfigure}
\caption{%
The geometrical angles used in the usual geometrical approach to the Abelian configuration do not distinguish among the possible branes orientations.
In fact we have $0 \le \alpha < 1$ and $0 < \varepsilon < 1$.
@@ -2552,8 +2577,7 @@ Each term of the action can be interpreted again as an area of a triangle where
\begin{figure}[tbp]
\centering
\def\svgwidth{0.35\textwidth}
\import{img/}{brane3d.pdf_tex}
\import{tikz}{brane3d.pgf}
\caption{%
Pictorial $3$-dimensional representation of two D2-branes intersecting in the Euclidean space $\R^3$ along a line (in $\R^4$ the intersection is a point since the co-dimension of each D-brane is 2): since it is no longer constrained on a bi-dimensional plane, the string must be deformed in order to stretch between two consecutive D-branes.
Its action can be larger than the planar area.

6
sec/part1/fermions.tex
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@@ -95,7 +95,7 @@ Their solutions are the ``holomorphic'' functions $\psi_{+}^i(\xi_+)$ and $\psi_
}
\begin{figure}[tbp]
\centering
\includegraphics[width=0.4\linewidth]{img/point-like-defects}
\import{tikz}{defects.pgf}
\caption{Propagation of the string in the presence of the worldsheet defects.}
\label{fig:point-like-defects}
\end{figure}
@@ -838,7 +838,7 @@ Finally we get the anti-commutation relations as
\begin{figure}[tbp]
\centering
\includegraphics[width=0.5\linewidth]{img/complex-plane}
\import{tikz}{complex_plane_defects.pgf}
\caption{%
Fields are glued on the $x < 0$ semi-axis with non trivial discontinuities for $x_{(t)} < x < x_{(t-1)}$ for $t = 1,\, 2,\, \dots,\, N$ and where $x_{(t)} = \exp( \htau_{E,\, (t)} )$.
}
@@ -1636,7 +1636,7 @@ Moreover notice that for $\rL \le -1$ both $b^{(\rE)}_{\rL \le n \le 0}$ and $b^
\begin{figure}[tbp]
\centering
\includegraphics[width=0.5\linewidth]{img/in-annihilators.pdf}
\import{tikz}{inconsistent_theories.pgf}
\caption{As a consistency condition, we have to exclude the values of
$\rL$ for which both $b^{(
E)}_n$ and $b^{*\, ( \brE )}_{\rL + 1 - n}$ are in-annihilators