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

TL;DR

This work shows that universal light-ray operators built from null integrals of the stress tensor in 4D Lorentzian CFTs realize the wedge subalgebra of ${\rm w}_{1+\infty}$, and that in theories with a continuous global symmetry they realize the ${S}$ algebra. By classifying light-ray operators according to scaling dimension $\Delta$ and ${\rm SL}(2,\mathbb{C})$ weights, the authors construct a tower of generators $\mathcal W^p$ that closes under a wedge ${\rm w}_{1+\infty}$ algebra, and a parallel tower $\mathcal S^{p,a}$ for spin-1 currents that closes under the ${S}$ algebra; the leading ANEC operator $\mathcal W^{3/2}$ and the Δ=0 primaries encode a BMS-like structure, with explicit commutators derived. A key result is the precise link between one-point functions of these light-ray generators in scalar states and universal soft factors from the infinite tower of soft graviton theorems, suggesting a deep connection between asymptotic symmetries and CFT data. The paper sets the stage for a longer companion work that will provide full proofs, a complete operator basis at fixed $\Delta$, and extensions to non-conformal theories and higher dimensions, with potential implications for celestial holography and AdS/CFT realizations.

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.