\( \mathcal{N}=2 \) supersymmetric gauge theories on S2 × S2 and Liouville Gravity

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 S2 × S2 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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Correspondence to Massimiliano Ronzani.

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ArXiv ePrint: 1411.2762

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Bawane, A., Bonelli, G., Ronzani, M. et al. \( \mathcal{N}=2 \) supersymmetric gauge theories on S2 × S2 and Liouville Gravity. J. High Energ. Phys. 2015, 54 (2015). https://doi.org/10.1007/JHEP07(2015)054

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Keywords

  • Supersymmetric gauge theory
  • Extended Supersymmetry
  • Topological Field Theories