Light-ray operators in conformal field theory

TL;DR

This paper introduces light-ray operators in conformal field theory, showing their role in analytic continuation of CFT data, deriving a Lorentzian OPE inversion formula, and extending the average null energy condition to continuous spin.

Contribution

It develops a novel framework for light-ray operators in CFT, generalizing the shadow transform, and extends conformal Regge theory and ANEC to continuous spin.

Findings

Derived a Lorentzian OPE inversion formula from light-ray operators.

Connected light-ray operators to the Regge limit of CFT correlators.

Provided a new proof and generalization of the average null energy condition.

Abstract

We argue that every CFT contains light-ray operators labeled by a continuous spin J. When J is a positive integer, light-ray operators become integrals of local operators over a null line. However for non-integer J, light-ray operators are genuinely nonlocal and give the analytic continuation of CFT data in spin described by Caron-Huot. A key role in our construction is played by a novel set of intrinsically Lorentzian integral transforms that generalize the shadow transform. Matrix elements of light-ray operators can be computed via the integral of a double-commutator against a conformal block. This gives a simple derivation of Caron-Huot's Lorentzian OPE inversion formula and lets us generalize it to arbitrary four-point functions. Furthermore, we show that light-ray operators enter the Regge limit of CFT correlators, and generalize conformal Regge theory to arbitrary four-point functions. The average null energy operator is an important example of a light-ray operator. Using our construction, we find a new proof of the average null energy condition (ANEC), and furthermore generalize the ANEC to continuous spin.