Non-singlet Q-deformation of the N=(1,1) gauge multiplet in harmonic superspace

TL;DR

This paper explores a specific non-anticommutative deformation of the N=(1,1) gauge multiplet in harmonic superspace, deriving explicit gauge and supersymmetry transformations, and analyzing the resulting bosonic action's structure.

Contribution

It provides a closed-form analysis of a non-singlet Q-deformation in harmonic superspace, including transformations and the bosonic sector of the invariant action.

Findings

Gauge transformations and unbroken supersymmetry are explicitly derived.

The bosonic action differs from the free action by a scalar factor involving a cosh function.

The deformation preserves a fraction of supersymmetry in special cases.

Abstract

We study a non-anticommutative chiral non-singlet deformation of the N=(1,1) abelian gauge multiplet in Euclidean harmonic superspace with a product ansatz for the deformation matrix, C^{(\alpha\beta)}_{(ik)} = c^{(\alpha\beta)}b_{(ik)}. This allows us to obtain in closed form the gauge transformations and the unbroken N=(1,0) supersymmetry transformations preserving the Wess-Zumino gauge, as well as the bosonic sector of the N=(1,0) invariant action. As in the case of a singlet deformation, the bosonic action can be cast in a form where it differs from the free action merely by a scalar factor. The latter is now given by \cosh^2 (2\bar\phi\sqrt{c^2 b^2}}), with \bar\phi being one of two scalar fields of the N=(1,1) vector multiplet. We compare our results with previous studies of non-singlet deformations, including the degenerate case b^2=0 which preserves the N=(1,1/2) fraction of N=(1,1) supersymmetry.