Some Aspects of Deformations of Supersymmetric Field Theories

TL;DR

This paper explores how Moyal-Weyl deformations of superspace affect supersymmetry, focusing on deformations of the Wess-Zumino model, abelian vector multiplet, and noncommutative U(1) gauge theories, revealing compatibility and limits.

Contribution

It provides new insights into the compatibility of supersymmetry with Moyal-Weyl deformations and extends the understanding of noncommutative supersymmetric gauge theories.

Findings

Deformation of Wess-Zumino model maintains supersymmetry.

Noncommutative abelian vector multiplet preserves key features.

Supersymmetric limit of Born-Infeld action relates to noncommutative U(1) gauge theory.

Abstract

We investigate some aspects of Moyal-Weyl deformations of superspace and their compatibility with supersymmetry. For the simplest case, when only bosonic coordinates are deformed, we consider a four dimensional supersymmetric field theory which is the deformation of the Wess-Zumino renormalizable theory of a chiral superfield. We then consider the deformation of a free theory of an abelian vector multiplet, which is a non commutative version of the rank one Yang-Mills theory. We finally give the supersymmetric version of the $\alpha'\mapsto 0$ limit of the Born-Infeld action with a B-field turned on, which is believed to be related to the non commutative U(1) gauge theory.