Graphical Representation of Supersymmetry

TL;DR

This paper introduces a graphical method for representing supersymmetry that simplifies spinor notation and clearly visualizes chiral flow, facilitating understanding and potential computational implementation across various SUSY theories.

Contribution

A novel graphical representation of supersymmetry using directed lines and wedges that simplifies spinor notation and is adaptable to multiple SUSY theories and dimensions.

Findings

Graphical method clearly expresses chiral flow in SUSY quantities.

Representation is applicable to Weyl and Majorana spinors.

Method is suitable for computer coding and diverse 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}. Both the Weyl spinor and the Majorana spinor are treated. We are free from the complicated 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.