Flat Holography: Aspects of the dual field theory

TL;DR

This paper explores the properties of a proposed dual field theory for flat spacetime, focusing on symmetry constraints and constructing examples that exhibit ultra-relativistic conformal invariance.

Contribution

It analyzes the symmetry structures of flat space holography, constructs correlators constrained by BMS4 symmetry, and presents new ultra-relativistic gauge theories as potential duals.

Findings

BMS4 symmetry constrains 3d correlators to resemble 2d CFT correlators.

Constructed examples of 4d field theories with ultra-relativistic conformal invariance.

Identified infinite ultra-relativistic conformal structures in Carrollian gauge theories.

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.