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

We study the SO(4)×SU(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 and scalar potentials for the hypermultiplets can be generated via the Scherk-Schwarz mechanism and Fayet-Iliopoulos term in analogy to the undeformed case.