File:N=2 R SCA unitary representations.svg

DescriptionN=2 R SCA unitary representations.svg	English: Allowed conformal weight (h) and R-charge (q) of unitary representations of N=2 superconformal algebra with R boundary conditions with central charge ${\displaystyle c=6}$. After Boucher, Friedan, Kent (1986) Phys Lett B 172:316 Eguchi, Taormina (1988) Phys Lett B 210: 125
Date	29 August 2015
Source	Own work
Author	Osteologia

LaTeX/TikZ source code:

\documentclass[tikz]{standalone}
\usepackage{tikz}
\usetikzlibrary{patterns,plotmarks}
\usepackage{mathpazo}
\begin{document}
\begin{tikzpicture}
%% c=6
\draw[->] (-3.8,0) -- (3.8,0) node[right] {\(q\)};
\draw[->] (0,-0.5) -- (0,5.5) node[above] {\(h\)};
\node at (3,5.5) {R, \(c=6\)};

\begin{scope}
\clip (-5,-1) rectangle (5,5);
%% h = q^2/2 - 7/8
\draw (0,-7/8) parabola (-5,{5^2/2-7/8});
\draw (0,-7/8) parabola (5,{5^2/2-7/8)});

%% double intersection points
%% q = half-integer
%% h = q^2/2 + 1/8
\coordinate (P0½) at ({0+1/2},{(0+1/2)^2/2+1/8});
\coordinate (P1½) at ({1+1/2},{(1+1/2)^2/2+1/8});
\coordinate (P2½) at ({2+1/2},{(2+1/2)^2/2+1/8});
\coordinate (P3½) at ({3+1/2},{(3+1/2)^2/2+1/8});
\coordinate (P4½) at ({4+1/2},{(4+1/2)^2/2+1/8});
\coordinate (P-0½) at ({-0-1/2},{(0+1/2)^2/2+1/8});
\coordinate (P-1½) at ({-1-1/2},{(1+1/2)^2/2+1/8});
\coordinate (P-2½) at ({-2-1/2},{(2+1/2)^2/2+1/8});
\coordinate (P-3½) at ({-3-1/2},{(3+1/2)^2/2+1/8});
\coordinate (P-4½) at ({-4-1/2},{(4+1/2)^2/2+1/8});

\draw[very thick, pattern=north west lines] (P-3½) -- (P-2½) -- (P-1½) -- (P-0½) -- (P0½) -- (P1½) -- (P2½) -- (P3½) -- cycle;

\fill (P0½) circle (2pt)
      (P-0½) circle (2pt)
      (P1½) circle (2pt)
      (P-1½) circle (2pt)
      (P2½) circle (2pt)
      (P-2½) circle (2pt)
      (P3½) circle (2pt)
      (P-3½) circle (2pt);

%% triple intersection points
%% q = half-integer
%% h = q^2/2 - 7/8
\coordinate (T1½) at ({1+1/2}, {(1+1/2)^2/2 - 7/8});
\coordinate (T2½) at ({2+1/2}, {(2+1/2)^2/2 - 7/8});
\coordinate (T3½) at ({3+1/2}, {(3+1/2)^2/2 - 7/8});
\coordinate (T-1½) at ({-1-1/2}, {(1+1/2)^2/2 - 7/8});
\coordinate (T-2½) at ({-2-1/2}, {(2+1/2)^2/2 - 7/8});
\coordinate (T-3½) at ({-3-1/2}, {(3+1/2)^2/2 - 7/8});

\draw [very thick] (P0½) -- plot [mark=x] (T1½);
\draw [thick, dashed] (T1½) -- (P3½);
\draw [very thick] (P1½) -- plot [mark=x] (T2½);
\draw [thick, dashed, mark=x] (T2½) -- (P4½);
\draw [very thick] (P2½) -- plot [mark=x] (T3½);

\draw [very thick] (P-0½) -- plot [mark=x] (T-1½);
\draw [thick, dashed] (T-1½) -- (P-3½);
\draw [very thick] (P-1½) -- plot [mark=x] (T-2½);
\draw [thick, dashed, mark=x] (T-2½) -- (P-4½);
\draw [very thick] (P-2½) -- plot [mark=x] (T-3½);
\end{scope}
\end{tikzpicture}
\end{document}

I, the copyright holder of this work, hereby publish it under the following license:

This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.

You are free:

• to share – to copy, distribute and transmit the work
• to remix – to adapt the work

Under the following conditions:

• attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
• share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

https://creativecommons.org/licenses/by-sa/4.0CC BY-SA 4.0 Creative Commons Attribution-Share Alike 4.0 truetrue