Non-anticommutative N=2 super-Yang-Mills theory with singlet deformation

We consider a non-anticommutative N=2 superspace with an SU(2) singlet and Lorentz scalar deformation parameter, ${theta^{alpha i},theta^{beta j}}_star = -2iP e^{alphabeta}e^{ij}$. We exploit this unique feature of the N=2 case to construct a deformation of the non-Abelian super-Yang-Mills theory which preserves the full N=2 supersymmetry together with the SU(2) R symmetry and Lorentz invariance. The resulting action describes a kind of heterotic special geometry with antiholomorphic prepotential $bar f(barphi) = Tr (barphi^2 (1+Pbarphi)^{-2})$.