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.
Highlights
In this paper we study a local version of the standard Poincaresymmetry algebra
Our main result is to determine the algebra obeyed by such light-ray operators using the elementary constraints of causality, unitarity, and Ward identities of Poincaresymmetries
In particular we show that the Bondi– van der Burg–Metzner–Sachs (BMS) algebra of [1,2,3] is a subalgebra of smeared versions of these light-ray operators
Summary
In this paper we study a local version of the standard Poincaresymmetry algebra. We consider nonlocal operators that are supported along a light ray and can be expressed as integrals of conserved currents. In the conformal collider setup of [9], this positivity is applied to constrain conformal field theory data such as operator product expansion (OPE) coefficients In our context these constraints mean that the physical representation of the algebra of light-ray operators on the Hilbert space enjoys positivity conditions analogous to unitarity constraints. By applying a conformal transformation, we can move this light sheet to future null infinity and the BMS algebra of light-ray operators manifests as generators of the asymptotic symmetries. Such operators are clearly connected to the insertion of soft gravitons since they are given by integrals of the energy-momentum tensor. We leave a more detailed investigation of this direction to future work
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