Holographic Symmetry Algebras for Gauge Theory and Gravity

TL;DR

The work develops a celestial CFT framework to classify non-trivial asymptotic symmetries in 4D gauge theory and gravity by constructing two infinite towers of positive-helicity conformally soft currents. It derives their OPEs and current algebras, revealing closed $SL(2,{\mathbb R})_R$ representations and holomorphic subalgebras, with gravity yielding a self-dual Lorentz subalgebra. The authors extend the algebra to include gluon-graviton interactions and connect the OPE structure to four-point MHV celestial amplitudes, providing a tangible bridge between celestial currents and standard scattering amplitudes. This subalgebra captures a rich, tractable portion of the full symmetry algebra and offers tools to organize asymptotic symmetries in gauge and gravity theories.

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.