Light-ray Operators and the ${\rm w}_{1+\infty}$ Algebra

TL;DR

This paper constructs universal light-ray operators in 4D conformal field theories that generate ${ m w}_{1+ abla}$ algebra and relates them to soft graviton theorems, revealing deep symmetry structures.

Contribution

It introduces universal classes of light-ray operators in 4D CFTs, generating ${ m w}_{1+ abla}$ and '$S$' algebras, and connects them to soft graviton theorems.

Findings

Light-ray operators generate ${ m w}_{1+ abla}$ algebra.

Additional operators generate the '$S$' algebra.

One-point functions relate to soft graviton theorems.

Abstract

A universal class of light-ray operators formed from null integrals of the stress tensor is constructed in generic interacting Lorentzian conformal field theories in four spacetime dimensions. This class of light-ray operators generates the wedge algebra of ${\rm w}_{1+\infty}$, which was recently identified among the asymptotic symmetries of asymptotically flat spacetimes. In four-dimensional conformal field theories with an additional spin-one conserved current, a second universal class of light-ray operators is constructed and shown to generate the ''$S$ algebra,'' the gauge-theoretic analog of ${\rm w}_{1+\infty}$. Finally, a precise relation is established between the one-point functions of these light-ray operators in scalar states and the universal soft factors in the infinite tower of soft graviton theorems. The results presented in this paper will be accompanied by detailed calculations and proofs in a longer forthcoming work.