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, {θ^αi,θ^βj}_★=-2iPɛ^αβɛ^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 f¯(φ¯)=Tr(φ¯²(1+Pφ¯)^-2).