Holographic Symmetry Algebras for Gauge Theory and Gravity

TL;DR

This paper constructs and classifies infinite-dimensional symmetry algebras in 4D gauge and gravity theories using 2D currents on the celestial sphere, revealing a rich structure related to soft theorems.

Contribution

It introduces two towers of 2D currents from helicity states, providing a systematic classification of symmetry algebras in asymptotically flat spacetimes.

Findings

Derived explicit current algebra commutators from OPE poles

Identified a closed subalgebra within the full symmetry algebra

Connected symmetry currents to conformally soft theorems

Abstract

All 4D gauge and gravitational theories in asymptotically flat spacetimes contain an infinite number of non-trivial symmetries. They can be succinctly characterized by generalized 2D currents acting on the celestial sphere. A complete classification of these symmetries and their algebras is an open problem. Here we construct two towers of such 2D currents from positive-helicity photons, gluons, or gravitons with integer conformal weights. These generate the symmetries associated to an infinite tower of conformally soft theorems. The current algebra commutators are explicitly derived from the poles in the OPE coefficients, and found to comprise a rich closed subalgebra of the complete symmetry algebra.