The BMS/GCA correspondence

TL;DR

This paper unveils a deep link between the asymptotic symmetries of flat spacetimes (BMS) and non-relativistic conformal algebras (GCA) by establishing explicit correspondences: BMS_3 is isomorphic to GCA_2 and BMS_4 corresponds to a semi-Galilean algebra gca^{s=1}_{3}. It analyzes central extensions and contrasts AdS-derived pictures with flat-space limits, including a BMN-type route that connects AdS shockingly to flat space while preserving boundary GCA structure. A general BMS/GCA correspondence is proposed, supported by concrete examples in 3D and 4D and extended via a semi-GCA framework; implications for flat-space holography and the S-matrix are discussed. The work sets a program to understand holography in flat spacetimes through non-relativistic conformal symmetries and motivates further study of representations and correlation functions in these dualities.

Abstract

We find a surprising connection between asymptotically flat space-times and non-relativistic conformal systems in one lower dimension. The BMS group is the group of asymptotic isometries of flat Minkowski space at null infinity. This is known to be infinite dimensional in three and four dimensions. We show that the BMS algebra in 3 dimensions is the same as the 2D Galilean Conformal Algebra which is of relevance to non-relativistic conformal symmetries. We further justify our proposal by looking at a Penrose limit of a radially infalling null ray inspired by non-relativistic scaling and obtain a flat metric. The 4D BMS algebra is also discussed and found to be the same as another class of GCA, called the semi-GCA, in three dimensions. We propose a general BMS/GCA correspondence. Some consequences are discussed.