Non‐Anticommutative Deformations of Gauge Fields and Hypermultiplets in N=(1,1) Superspace

We overview the SO(4)×SU(2) invariant and N=(1,0) supersymmetry‐preserving non‐anticommutative deformations of the Euclidean N=(1,1) supersymmetric gauge theories and hypermultiplets (neutral and charged) interacting with an abelian gauge multiplet, starting from their off‐shell formulation in N=(1,1) harmonic superspace. The corresponding component actions are presented and the Seiberg‐Witten‐type transformations to the undeformed component fields are explicitly given. 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. The neutral hypermultiplet action is invariant under N=(2,0) supersymmetry and describes a deformed N=(2,2) gauge theory. The string theory origin of the considered singlet deformation is exhibited.