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, $\{\theta^{\alpha i}, \theta^{\beta j}\}_\star = -2iP \epsilon^{\alpha\beta}\epsilon^{ij}$. We exploit this unique feature of the N=2 case to construct a deformation of the rank-one 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 $\bar(\bar\phi) = \bar\phi^2 (1+P\bar\phi)^{-2}$.