Transverse spin in the light-ray OPE

We study a product of null-integrated local operators O-1 and O-2 on the same null plane in a CFT. Such null-integrated operators transform like primaries in a fictitious d - 2 dimensional CFT in the directions transverse to the null integrals. We give a complete description of the OPE in these transverse directions. The terms with low transverse spin are light-ray operators with spin J(1) + J(2) - 1. The terms with higher transverse spin are primary descendants of light-ray operators with higher spins J(1) + J(2) - 1 + n, constructed using special conformally-invariant differential operators that appear precisely in the kinematics of the light-ray OPE. As an example, the OPE between average null energy operators contains light-ray operators with spin 3 (as described by Hofman and Maldacena), but also novel terms with spin 5, 7, 9, etc. These new terms are important for describing energy two-point correlators in non-rotationally-symmetric states, and for computing multi-point energy correlators. We check our formulas in a non-rotationally-symmetric energy correlator in N = 4 SYM, finding perfect agreement.

Automated summary

We studied the properties of the product of null-integrated local operators on the same null plane in a conformal field theory (CFT). These null-integrated operators transform similarly to primaries in a fictitious (d-2)-dimensional CFT in the directions transverse to the null integrals. We provided a complete description of the operator product expansion (OPE) in these transverse directions, where the terms with low transverse spin correspond to light-ray operators and the terms with higher transverse spin are the primary descendants. These findings are important for describing non-rotationally-symmetric states and computing multi-point energy correlators.