Vector-multiplet effective action in the non-anticommutative charged   hypermultiplet model
  We investigate the quantum aspects of a charged hypermultiplet in deformed N=(1,1) superspace with singlet non-anticommutative deformation of supersymmetry. This model is a "star" modification of the hypermultiplet interacting with a background Abelian vector superfield. We prove that this model is renormalizable in the sense that the divergent part of the effective action is proportional to the N=(1,0) non-anticommutative super Yang-Mills action. We also calculate the finite part of the low-energy effective action depending on the vector multiplet, which corresponds to the (anti)holomorphic potential. The holomorphic piece is just deformed to the star-generalization of the standard holomorphic potential, while the antiholomorphic piece is not. We also reveal the component structure and find the deformation of the mass and the central charge. 
I.L. Buchbinder, O. Lechtenfeld, I.B. Samsonov