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Twisting with a Flip (the Art of Pestunization)
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Twisting with a Flip (the Art of Pestunization)
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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. We conjecture the full partition function for a ${\cal N}=2$ theory on any 4D manifold with a Killing vector. Using this new notion of self-duality to localize a supersymmetric theory is what we call "Pestunization".
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Cited by 1 Pith paper
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Contour Integral for the Partition Function of $\mathcal{N}=2$ Topologically Twisted on $\mathbb{CP}^2$ and Physical Fluxes
Derives a single-flux contour-integral formula for the N=2 twisted SU(2) partition function on CP^2 and new equivariant invariants reducing to Donaldson invariants.
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