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The gravity/CFT correspondence

  • Regular Article - Theoretical Physics
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Abstract

General Relativity can be formulated in terms of a spatially Weyl invariant gauge theory called Shape Dynamics. Using this formulation, we establish a “bulk/bulk” duality between gravity and a Weyl invariant theory on spacelike Cauchy hypersurfaces. This duality has two immediate consequences: (i) it leads trivially to a corresponding “bulk/boundary” duality between General Relativity and a boundary CFT, and (ii) the boundary can be defined in a gauge-invariant way. Moreover, the corresponding bulk/boundary duality is sufficient to explain a large portion of the evidence in favor of gauge/gravity duality and provides independent evidence for the AdS/CFT correspondence.

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Notes

  1. By “local” we mean involving only a finite number of derivatives.

  2. These conditions are compatible with asymptotic (in time) dS space, which has maximally symmetric CMC slices.

  3. In even dimensions, there would be a (finite) V-independent piece that resembles a conformal anomaly.

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Acknowledgements

We would like to thank Julian Barbour for his unique vision and perseverance towards finding a scale–free description of gravity, Lee Smolin for encouraging us to explore the link between shape dynamics and the gravity/CFT correspondence, and Laurent Freidel for useful discussions. Research at the Perimeter Institute is supported in part by the Government of Canada through NSERC and by the Province of Ontario through MEDT. This work was funded, in part, by a grant from the Foundational Questions Institute (FQXi) Fund, a donor advised fund of the Silicon Valley Community Foundation on the basis of proposal FQXi-RFP2-08-05 to the Foundational Questions Institute. HG was supported in part by the U.S. Department of Energy under grant DE-FG02-91ER40674.

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Authors and Affiliations

  1. University of California at Davis, One Shields Avenue, Davis, CA, 95616, USA

    Henrique Gomes

  2. Utrecht University, Leuvenlaan 4, 3584 CE, Utrecht, The Netherlands

    Sean Gryb

  3. Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5, Canada

    Tim Koslowski & Flavio Mercati

  4. Dept. of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3, Canada

    Tim Koslowski

  5. Departamento de Física Teórica, Universidad de Zaragoza, Zaragoza, 50009, Spain

    Flavio Mercati

  6. School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK

    Flavio Mercati

Authors
  1. Henrique Gomes
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  2. Sean Gryb
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  3. Tim Koslowski
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  4. Flavio Mercati
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Correspondence to Sean Gryb.

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Gomes, H., Gryb, S., Koslowski, T. et al. The gravity/CFT correspondence. Eur. Phys. J. C 73, 2275 (2013). https://doi.org/10.1140/epjc/s10052-013-2275-3

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