Non-anticommutative deformation of N=(1,1) hypermultiplets

TL;DR

This paper explores a specific non-anticommutative deformation of hypermultiplets in supersymmetric gauge theories, preserving certain symmetries and providing explicit component actions and transformations, extending the understanding of deformed supersymmetric models.

Contribution

It introduces a new SO(4)xSU(2) invariant non-anticommutative deformation of hypermultiplets within Euclidean N=(1,1) harmonic superspace, detailing their actions and symmetry properties.

Findings

Deformed hypermultiplet actions are explicitly derived.

Seiberg-Witten-type transformations are provided.

Mass terms can be generated via Scherk-Schwarz and Fayet-Iliopoulos mechanisms.

Abstract

We study the SO(4)xSU(2) invariant and N=(1,0) supersymmetry-preserving nilpotent (non-anticommutative) Moyal deformation of hypermultiplets interacting with an abelian gauge multiplet, starting from their off-shell formulation in Euclidean N=(1,1) harmonic superspace. The deformed version of a neutral or a charged hypermultiplet corresponds to the `adjoint' or the `fundamental' representation of the deformed U(1) gauge group on the superfields involved. The neutral hypermultiplet action is invariant under N=(2,0) supersymmetry and describes a deformed N=(2,2) gauge theory. For both the neutral and the charged hypermultiplet we present the corresponding component actions and explicitly give the Seiberg-Witten-type transformations to the undeformed component fields. Mass terms for the hypermultiplets can be generated via the Scherk-Schwarz mechanism and Fayet-Iliopoulos term in analogy to the undeformed case.