Supersymmetric Gauge Theories on Noncommutative Superspace

TL;DR

This paper develops supersymmetric gauge theories on noncommutative superspace, constructing actions for N=1 and N=2 super Yang-Mills theories, revealing that noncommutativity reduces supersymmetry to N=1/2.

Contribution

It introduces explicit constructions of supersymmetric gauge theories on noncommutative superspace, extending previous work and analyzing supersymmetry preservation.

Findings

N=1 super Yang-Mills action with full supersymmetry on noncommutative superspace

N=2 super Yang-Mills action with reduced N=1/2 supersymmetry

Demonstration that noncommutativity breaks supersymmetry from N=1/2 to N=1/2 for N=2 theories

Abstract

We study four dimensional supersymmetric gauge theory on the noncommutative superspace, recently proposed by Seiberg. We construct the gauge-invariant action of N=1 super Yang-Mills theory with chiral and antichiral superfields, which has N=1/2 supersymmetry on the noncommutative superspace. We also construct the action of N=2 super Yang-Mills theory. It is shown that this theory has only N=1/2 supersymmetry.