Twisting with a Flip (the Art of Pestunization)

Authors: Guido Festuccia, Jian Qiu, Jacob Winding, Maxim Zabzine Preprint number: UUITP-59/18  We construct  N=2 supersymmetric Yang-Mills theory on 4D manifold with Killing vector field with the isolated fixed points. It turns out that for every fixed point one can allocate either instanton or anti-instanton contributions in the partition function and this is compatible with the supersymmetry. The equivariant Donaldson-Witten theory is a special case of our construction. We present the unified treatment of the Pestun's calculation on S^4 and the equivariant Donaldson-Witten theory by generalizing the notion of self-duality on the manifolds with a vector field. We conjecture the full partition function for N=2 theory on any 4D simply connected manifold with a Killing vector.