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BMS/GCA redux: towards flatspace holography from non-relativistic symmetries

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Abstract

The asymptotic group of symmetries at null infinity of flat spacetimes in three and four dimensions is the infinite dimensional Bondi-Metzner-Sachs (BMS) group. This has recently been shown to be isomorphic to non-relativistic conformal algebras in one lower dimension, the Galilean Conformal Algebra (GCA) in 2d and a closely related non-relativistic algebra in 3d [1, 2]. We provide a better understanding of this surprising connection by providing a spacetime interpretation in terms of a novel contraction. The 2d GCA was previously obtained from a linear combination of two copies of the Virasoro algebra. We consider a representation obtained from a different linear combination of the Virasoros, which is relevant to the relation with the BMS algebra in three dimensions. This is realised by a new space-time contraction of the parent algebra. We show that this representation has interesting correlation functions. We discuss implications for the BMS/GCA correspondence and show that the flat space limit actually induces precisely this contraction on the boundary conformal field theory. We also discuss aspects of asymptotic symmetries and the consequences of this contraction in higher dimensions.

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Authors and Affiliations

  1. School of Mathematics, University of Edinburgh, Kings Buildings, Edinburgh, EH9 3JZ, United Kingdom

    Arjun Bagchi

  2. School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran

    Reza Fareghbal

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  1. Arjun Bagchi
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Correspondence to Arjun Bagchi.

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ArXiv ePrint: 1203.5795

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Bagchi, A., Fareghbal, R. BMS/GCA redux: towards flatspace holography from non-relativistic symmetries. J. High Energ. Phys. 2012, 92 (2012). https://doi.org/10.1007/JHEP10(2012)092

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