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

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arxiv 1411.2762 v3 pith:NGRSMZCH submitted 2014-11-11 hep-th math-phmath.AGmath.MPmath.RT

Aditya Bawane , Giulio Bonelli , Massimiliano Ronzani , Alessandro Tanzini This is my paper · ORCID
classification hep-thmath-phmath.AGmath.MPmath.RT
keywords supersymmetricadmittingblocksfourgaugegravityisometryliouville
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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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Cited by 4 Pith papers

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