N=1/2 Supersymmetric gauge theory in noncommutative space

TL;DR

This paper develops a formulation of N=1/2 supersymmetric U(N) gauge theory in noncommutative space, analyzing one-loop UV/IR mixing and extending the Seiberg-Witten map to non-anticommutative superspace.

Contribution

It introduces a new approach to formulate supersymmetric gauge theories in noncommutative space, including a generalized Seiberg-Witten map and analysis of supersymmetry transformations.

Findings

UV/IR mixing occurs at one loop.

A generalized Seiberg-Witten map is constructed.

Supersymmetry transformations are local for abelian and non-local for non-abelian theories.

Abstract

A formulation of (non-anticommutative) N=1/2 supersymmetric U(N) gauge theory in noncommutative space is studied. We show that at one loop UV/IR mixing occurs. A generalization of Seiberg-Witten map to noncommutative and non-anticommutative superspace is employed to obtain an action in terms of commuting fields at first order in the noncommutativity parameter tetha. This leads to abelian and non-abelian gauge theories whose supersymmetry transformations are local and non-local, respectively.