Graphical Representation of Supersymmetry

TL;DR

This paper introduces a graphical method for representing supersymmetry that simplifies the visualization of chiral flow and spinor structures, making it suitable for computational implementation across various SUSY theories.

Contribution

It presents a novel graphical representation of supersymmetry using directed lines and wedges, enabling clearer visualization and easier coding for diverse SUSY models.

Findings

Graphical method clearly expresses chiral flow in SUSY quantities.

Representation is applicable to multiple dimensions and theories, including supergravity.

Method facilitates computer programming and understanding of complex SUSY structures.

Abstract

A graphical representation of supersymmetry is presented. It clearly expresses the chiral flow appearing in SUSY quantities, by representing spinors by {\it directed lines} (arrows). The chiral suffixes are expressed by the directions (up, down, left, right) of the arrows. The SL(2,C) invariants are represented by {\it wedges}. Both the Weyl spinor and the Majorana spinor are treated. We are free from the messy symbols of spinor suffixes. The method is applied to the 5D supersymmetry. Many applications are expected. The result is suitable for coding a computer program and is highly expected to be applicable to various SUSY theories (including Supergravity) in various dimensions.