Twisting with a Flip (the Art of Pestunization)

Abstract

We construct $\mathcal{N}=2$ 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 $\mathcal{N}=2$ 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".

58 pages, typos corrected, the final version to appear in CMP

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• The joy of factorization at large $N$: five-dimensional indices and AdS black holes
• Effective gravitational couplings of four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories
• SYM on Quotients of Spheres and Complex Projective Spaces
• Cohomological Localization of $\mathcal{N}=2$ Gauge Theories with Matter
• Gauge theories on compact toric manifolds
• Partition Functions and Fibering Operators on the Coulomb Branch of 5d SCFTs
• Super Yang-Mills on Branched Covers and Weighted Projective Spaces
• Conformal field theories on deformed spheres, anomalies, and supersymmetry
• Maximally symmetric nuts in 4d $\mathcal{N}=2$ higher derivative supergravity
• S-duality and supersymmetry on curved manifolds
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• Exact Results for SYM on $Y^{p,q}$ and $S^2\times S^2$ with Conical Singularities
• Index of the Transversally Elliptic Complex in Pestunization
• From 5d Flat Connections to 4d Fluxes (the Art of Slicing the Cone)
• Algebras, traces, and boundary correlators in $\mathcal{N}=4$ SYM
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