Non-anticommutative chiral singlet deformation of N=(1,1) gauge theory

TL;DR

This paper investigates a specific deformation of N=(1,1) gauge theories that preserves some supersymmetry features while breaking others, providing explicit component actions and nonlinear field redefinitions for certain gauge groups.

Contribution

It introduces a novel SO(4)x SU(2) invariant Q-deformation of Euclidean N=(1,1) gauge theories, detailing the resulting actions and Seiberg-Witten maps for U(1) and U(n) groups.

Findings

Explicit component form of the deformed gauge action for U(1) and U(n)

Existence of nonlinear Seiberg-Witten maps relating deformed and undeformed multiplets

Deformed U(n) gauge theory can be reduced to SU(n) via nonlinear transformations

Abstract

We study the SO(4)x SU(2) invariant Q-deformation of Euclidean N=(1,1) gauge theories in the harmonic superspace formulation. This deformation preserves chirality and Grassmann harmonic analyticity but breaks N=(1,1) to N=(1,0) supersymmetry. The action of the deformed gauge theory is an integral over the chiral superspace, and only the purely chiral part of the covariant superfield strength contributes to it. We give the component form of the N=(1,0) supersymmetric action for the gauge groups U(1) and U(n>1). In the U(1) and U(2) cases, we find the explicit nonlinear field redefinition (Seiberg-Witten map) relating the deformed N=(1,1) gauge multiplet to the undeformed one. This map exists in the general U(n) case as well, and we use this fact to argue that the deformed U(n) gauge theory can be nonlinearly reduced to a theory with the gauge group SU(n).