BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries

TL;DR

This paper explores the connection between BMS symmetries in flat spacetimes and non-relativistic conformal algebras, providing a spacetime interpretation through a novel contraction and analyzing implications for flat space holography.

Contribution

It introduces a new spacetime contraction that reveals a unitary subsector in the GCA related to BMS symmetries, advancing understanding of flat space holography.

Findings

A new contraction relates BMS and GCA algebras.

Identification of a unitary subsector with non-trivial correlation functions.

Flat space limit induces this contraction on the boundary CFT.

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]. We provide a better understanding of this surprising connection by providing a spacetime interpretation in terms of a novel contraction. The 2d GCA, obtained from a linear combination of two copies of the Virasoro algebra, is generically non-unitary. The unitary subsector previously constructed had trivial correlation functions. 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 a unitary sub-sector with 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.