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Supersymmetry in Lorentzian Curved Spaces and Holography

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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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