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, $\{θ^{αi},θ^{βj}\}_\star = -2iP \e^{αβ}\e^{ij}$. 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 $\bar f(\barϕ) = Tr (\barϕ^2 (1+P\barϕ)^{-2})$.

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