Twisting with a Flip (the Art of Pestunization)

Understand

We construct ${\cal N}=2$ supersymmetric Yang-Mills theory on 4D manifolds with a Killing vector field with isolated fixed points.

• It turns out that for every fixed point one can allocate either instanton or anti-instanton contributions to the partition function, and that this is compatible with supersymmetry.
• The equivariant Donaldson-Witten theory is a special case of our construction.
• We present a unified treatment of Pestun's calculation on $S^4$ and equivariant Donaldson-Witten theory by generalizing the notion of self-duality on manifolds with a vector field.