Light-ray Operators and the BMS Algebra

TL;DR

This paper explores the algebraic structure of light-ray operators in conformal field theories, revealing that the generalized BMS algebra is a subalgebra of the light-ray operator algebra, with verification in free scalar theories.

Contribution

It determines the light-ray operator algebra in conformal field theories and shows its relation to the generalized BMS algebra, including supertranslations and superrotations.

Findings

The light-ray operators form an infinite-dimensional algebra.

The generalized BMS algebra is a subalgebra of the light-ray algebra.

Verification of the algebra in free scalar field theory.

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.