$\mathcal{N}=2$ supersymmetric gauge theories on $S^2\times S^2$ and Liouville Gravity

Aditya Bawane; Giulio Bonelli; Massimiliano Ronzani; Alessandro Tanzini

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arXiv · 1411.2762

$\mathcal{N}=2$ supersymmetric gauge theories on $S^2\times S^2$ and Liouville Gravity

Aditya Bawane·Giulio Bonelli·Massimiliano Ronzani·Alessandro Tanzini

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Abstract

We consider $\mathcal{N}=2$ supersymmetric gauge theories on four manifolds admitting an isometry. Generalized Killing spinor equations are derived from the consistency of supersymmetry algebrae and solved in the case of four manifolds admitting a $U(1)$ isometry. This is used to explicitly compute the supersymmetric path integral on $S^2\times S^2$ via equivariant localization. The building blocks of the resulting partition function are shown to contain the three point functions and the conformal blocks of Liouville Gravity.

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Aditya Bawane, Giulio Bonelli, Massimiliano Ronzani, Alessandro Tanzini. 2014-11-11. $\mathcal{N}=2$ supersymmetric gauge theories on $S^2\times S^2$ and Liouville Gravity. https://arxiv.org/abs/1411.2762

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