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\( \mathcal{N}=2 \) supersymmetric gauge theories on S2 × S2 and Liouville Gravity
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  • Regular Article - Theoretical Physics
  • Open Access
  • Published: 13 July 2015

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

  • Aditya Bawane1,2,
  • Giulio Bonelli1,2,
  • Massimiliano Ronzani1,2 &
  • …
  • Alessandro Tanzini1,2 

Journal of High Energy Physics volume 2015, Article number: 54 (2015) Cite this article

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A preprint version of the article is available at arXiv.

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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This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Authors and Affiliations

  1. International School of Advanced Studies (SISSA), via Bonomea 265, 34136, Trieste, Italy

    Aditya Bawane, Giulio Bonelli, Massimiliano Ronzani & Alessandro Tanzini

  2. INFN, Sezione di Trieste, Trieste, Italy

    Aditya Bawane, Giulio Bonelli, Massimiliano Ronzani & Alessandro Tanzini

Authors
  1. Aditya Bawane
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  2. Giulio Bonelli
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  3. Massimiliano Ronzani
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  4. Alessandro Tanzini
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Correspondence to Massimiliano Ronzani.

Additional information

ArXiv ePrint: 1411.2762

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Cite this article

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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  • Received: 21 January 2015

  • Revised: 15 May 2015

  • Accepted: 15 June 2015

  • Published: 13 July 2015

  • DOI: https://doi.org/10.1007/JHEP07(2015)054

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Keywords

  • Supersymmetric gauge theory
  • Extended Supersymmetry
  • Topological Field Theories
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