Light-ray operators and the BMS algebra

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) Bondi--van der Burg--Metzner--Sachs algebra, including both the supertranslation and the super-rotation, 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.