Duals of noncommutative supersymmetric U(1) gauge theory

TL;DR

This paper derives the dual of noncommutative supersymmetric U(1) gauge theory in 4D, explores the generalized Seiberg-Witten map, and discusses the breaking of duality symmetry at the action level.

Contribution

It introduces a parent action framework for noncommutative supersymmetric U(1) gauge theory and analyzes the duality symmetry and its breaking in this context.

Findings

Duals of noncommutative supersymmetric U(1) gauge theory are obtained.

Duality symmetry is broken at the action level due to noncommutativity.

A noncommutative parent action preserving duality symmetry is proposed.

Abstract

Parent actions for component fields are utilized to derive the dual of supersymmetric U(1) gauge theory in 4 dimensions. Generalization of the Seiberg-Witten map to the component fields of noncommutative supersymmetric U(1) gauge theory is analyzed. Through this transformation we proposed parent actions for noncommutative supersymmetric U(1) gauge theory as generalization of the ordinary case.Duals of noncommutative supersymmetric U(1) gauge theory are obtained. Duality symmetry under the interchange of fields with duals accompanied by the replacement of the noncommutativity parameter \Theta_{\mu\nu} with \tilde{\Theta}_{\mu \nu} = \epsilon_{\mu\nu\rho\sigma}\Theta^{\rho\sigma} of the non--supersymmetric case is broken at the level of actions. We proposed a noncommutative parent action for the component fields which generates actions possessing this duality symmetry.