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

By Arjun Bagchi, R. Fareghbal. 2012

215 citations recorded by the source corpus.

A bstractThe 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c3e2f779ba51da2d526af7bf6c3f5042f4ff934e

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Citations in the corpus

Lessons from the information paradox (2020, background): “This is just part of a broader program of understanding how holography works in flat space, including the question of how asymptotic symmetries constrain asymptotic correlators and other physical quantities [95–101] on which there is significant literature starting with the work of de Boer and Solod”
Warped Conformal Field Theory (2012, background): “Much effort has been dedicated to the study of flat (see [10, 11, 12, 13, 14, 15, 16, 17, 18] for example) and de Sitter (see e.”
Gauging the Carroll algebra and ultra-relativistic gravity (2015, background): “In 3 bulk dimensions it has been shown that the BMS algebra is isomorphic to the 2-dimensional Galilean conformal algebra [55, 56] (which is a contraction of the relativistic conformal group [57]).”
The Holographic Nature of Null Infinity (2020, background): “It is somewhat remarkable that the BMS algebra can indeed be recovered as a limit of a (non-relativistic) conformal algebra in this manner [55, 9].”
Tensionless strings from worldsheet symmetries (2015, methodology): “This proposal, which at times goes under the name of the BMS/GCA correspondence, has been successfully employed to understand several aspects of bulk physics in flat space [64]–[70].”
Tensionless strings and Galilean Conformal Algebra (2013, background): “The spacetime symmetry, or in more precise words the asymptotic symmetry group of AdS3 is two copies of the infinite dimensional Virasoro algebra.”
Conformal Carroll groups (2014, background): “8) In [14] it has been shown how cgal2(1 + 1) arises as a “non-relativistic contraction” of two (centre-free) Virasoro algebras, i.”
Dynamics of Carroll particles (2014, background): “The BMS algebra [7] has emerged recently as the boundary symmetry group in a study of flat space holography, see for example [8, 9].”
Flat holography: aspects of the dual field theory (2016, background): “For the D = 3 case, the exercise is a bit more involved [31].”