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Supersymmetry in Lorentzian Curved Spaces and Holography

Communications in Mathematical Physics volume 327, pages 577–602 (2014)Cite this article

Abstract

We consider superconformal and supersymmetric field theories on four-dimensional Lorentzian curved space-times, and their five-dimensional holographic duals. As in the Euclidean signature case, preserved supersymmetry for a superconformal theory is equivalent to the existence of a charged conformal Killing spinor. Differently from the Euclidean case, we show that the existence of such spinors is equivalent to the existence of a null conformal Killing vector. For a supersymmetric field theory with an R-symmetry, this vector field is further restricted to be Killing. We demonstrate how these results agree with the existing classification of supersymmetric solutions of minimal gauged supergravity in five dimensions.

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Authors and Affiliations

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

    Davide Cassani & Dario Martelli

  2. Dipartimento di Fisica, Università di Milano-Bicocca, 20126, Milano, Italy

    Claudius Klare, Alessandro Tomasiello & Alberto Zaffaroni

  3. INFN, Sezione di Milano-Bicocca, 20126, Milano, Italy

    Claudius Klare, Alessandro Tomasiello & Alberto Zaffaroni

Authors
  1. Davide Cassani
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  2. Claudius Klare
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  3. Dario Martelli
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  4. Alessandro Tomasiello
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  5. Alberto Zaffaroni
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Correspondence to Davide Cassani.

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Communicated by N. A. Nekrasov

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Cassani, D., Klare, C., Martelli, D. et al. Supersymmetry in Lorentzian Curved Spaces and Holography. Commun. Math. Phys. 327, 577–602 (2014). https://doi.org/10.1007/s00220-014-1983-3

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  • DOI: https://doi.org/10.1007/s00220-014-1983-3

Keywords

  • Conformal Killing
  • Superconformal Theory
  • Supersymmetric Solution
  • Conformal Supergravity
  • Minimal Supergravity