BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries
Arjun Bagchi, Reza Fareghbal
TL;DR
This work establishes a concrete spacetime realization of the BMS/GCA correspondence by introducing a time-directed contraction that yields a unitary, nontrivial 2d Galilean Conformal Algebra (GCA) representation. It shows that the flat-space limit of AdS$_3$ induces this contraction on the boundary CFT, reproducing the BMS$_3$ algebra as the asymptotic symmetry and relating it to the GCA in two dimensions. The authors compute nontrivial boundary correlators in the new GCA representation, analyze unitarity and null vectors, and discuss connections to non-relativistic hydrodynamics and turbulence. They also discuss bulk interpretations via Killing vectors and asymptotic symmetry analyses, and outline implications for higher dimensions and future flat-space holography research, including potential paths toward a boundary S-matrix. Overall, the paper advances a coherent framework connecting flat space holography, non-relativistic conformal symmetries, and bulk/boundary contractions.
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.