Graphical Representation of Supersymmetry and Computer Calculation

TL;DR

This paper introduces a graphical method for representing supersymmetry, using directed lines and wedges to simplify complex spinor expressions, facilitating computer coding and application across various SUSY theories.

Contribution

It presents a novel graphical representation of supersymmetry that simplifies spinor expressions and is adaptable for computer implementation in diverse SUSY theories.

Findings

Graphical representation clearly expresses chiral flow.

Method is applicable to 5D supersymmetry and beyond.

Suitable for computer programming and various SUSY theories.

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}. 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.