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Gravity duals of supersymmetric gauge theories on three-manifolds

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  • Published: 11 August 2016
  • Volume 2016, article number 80, (2016)
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Gravity duals of supersymmetric gauge theories on three-manifolds
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  • Daniel Farquet1,
  • Jakob Lorenzen2,
  • Dario Martelli2 &
  • …
  • James Sparks1 

A preprint version of the article is available at arXiv.

Abstract

We study gravity duals to a broad class of \( \mathcal{N} \) = 2 supersymmetric gauge theories defined on a general class of three-manifold geometries. The gravity backgrounds are based on Euclidean self-dual solutions to four-dimensional gauged supergravity. As well as constructing new examples, we prove in general that for solutions defined on the four-ball the gravitational free energy depends only on the supersymmetric Killing vector, finding a simple closed formula when the solution has U(1) × U(1) symmetry. Our result agrees with the large N limit of the free energy of the dual gauge theory, computed using localization. This constitutes an exact check of the gauge/gravity correspondence for a very broad class of gauge theories with a large N limit, defined on a general class of background three-manifold geometries.

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Authors and Affiliations

  1. Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK

    Daniel Farquet & James Sparks

  2. Department of Mathematics, King’s College London, The Strand, London, WC2R 2LS, UK

    Jakob Lorenzen & Dario Martelli

Authors
  1. Daniel Farquet
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  2. Jakob Lorenzen
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Correspondence to Dario Martelli.

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ArXiv ePrint: 1404.0268

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Cite this article

Farquet, D., Lorenzen, J., Martelli, D. et al. Gravity duals of supersymmetric gauge theories on three-manifolds. J. High Energ. Phys. 2016, 80 (2016). https://doi.org/10.1007/JHEP08(2016)080

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  • Received: 20 June 2016

  • Accepted: 04 August 2016

  • Published: 11 August 2016

  • DOI: https://doi.org/10.1007/JHEP08(2016)080

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Keywords

  • Gauge-gravity correspondence
  • Supersymmetric gauge theory
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