Flat Holography: Aspects of the dual field theory

TL;DR

The paper investigates flat-space holography by examining how asymptotic BMS4 symmetries constrain a putative 3d boundary theory dual to 4d Minkowski space, showing that 2d CFT-like two- and three-point functions arise from BMS4 highest-weight representations. It then develops ultra-relativistic contractions of the conformal algebra to define the conformal Carroll algebra (CCA) and its infinite extension, i-CCA, exploring their representations. The authors construct Carrollian limits of gauge theories (electrodynamics and Yang–Mills) in D=4, demonstrate invariance under Conformal Carroll symmetries across multiple UR sectors, and argue that these UR theories furnish prototypical duals to higher-dimensional flat spacetimes. Overall, the work provides a cohesive framework for flat-space holography via BMS/Carrollian symmetries and identifies promising directions for matter coupling, actions, and connections to tensionless/stringy regimes.

Abstract

Assuming the existence of a field theory in D dimensions dual to (D+1)-dimensional flat space, governed by the asymptotic symmetries of flat space, we make some preliminary remarks about the properties of this field theory. We review briefly some successes of the 3d bulk - 2d boundary case and then focus on the 4d bulk - 3d boundary example, where the symmetry in question is the infinite dimensional BMS4 algebra. We look at the constraints imposed by this symmetry on a 3d field theory by constructing highest weight representations of this algebra. We construct two and three point functions of BMS primary fields and surprisingly find that symmetries constrain these correlators to be identical to those of a 2d relativistic conformal field theory. We then go one dimension higher and construct prototypical examples of 4d field theories which are putative duals of 5d Minkowski spacetimes. These field theories are ultra-relativistic limits of electrodynamics and Yang-Mills theories which exhibit invariance under the conformal Carroll group in D=4. We explore the different sectors within these Carrollian gauge theories and investigate the symmetries of the equations of motion to find that an infinite ultra-relativistic conformal structure arises in each case.