Light-ray Operators and the BMS Algebra

TL;DR

This work derives a universal infinite-dimensional algebra for light-ray operators constructed from the stress-energy tensor in any unitary CFT, showing that smeared light-ray charges on a light-sheet generate a subalgebra isomorphic to the generalized BMS algebra in $d$ dimensions. By combining microcausality, unitarity, Ward identities, and a minimal Closure assumption, the authors compute the full commutator algebra among ${\cal E}$, ${\cal K}$, and ${\cal N}_A$, and demonstrate how smeared versions recover the BMS generators ${\cal T}(f)$ and ${\cal R}(Y^A)$. They extend the construction to non-abelian spin-one currents and verify the algebra in free field theory as a concrete consistency check, including subtleties arising from placing operators on the same light-sheet. The results connect null energy, asymptotic symmetries, and quantum information perspectives, highlighting a universal structure governing non-local light-ray observables and their potential links to soft theorems and memory effects.

Abstract

We study light-ray operators constructed from the energy-momentum tensor in $d$-dimensional Lorentzian conformal field theory. These include in particular the average null energy operator. The commutators of parallel light-ray operators on a codimension one light-sheet form an infinite-dimensional algebra. We determine this light-ray algebra and find that the $d$-dimensional (generalized) BMS algebra, including both the supertranslation and the superrotation, is a subalgebra. We verify this algebra in correlation functions of free scalar field theory. We also determine the infinite-dimensional algebra of light-ray operators built from non-abelian spin-one conserved currents.