Twisting with a flip (The art of pestunization)

DOI10.1007/S00220-020-03681-9zbMATH Open1440.81065arXiv1812.06473OpenAlexW3103091133WikidataQ126293863 ScholiaQ126293863MaRDI QIDQ2186077

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Publication date: 9 June 2020

Published in: (Search for Journal in Brave)

Abstract: We construct $calN=2$ 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 $calN=2$ 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".

Full work available at URL: https://arxiv.org/abs/1812.06473

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