Transverse spin in the light-ray OPE

Abstract

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 lightray 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.

Distributions in CFT II. Minkowski Space

“…These operators are defined for generic complex and reduce to light-transforms (null integrals) of local operators for integer spins. More recently, light-ray operators have been used to understand an OPE for event-shape observables such as energy-energy correlators in CFT [122][123][124] (see also [125,126]). The light-ray operators correspond to poles in ∆ of C(∆, ), and the issues with convergence of LIF described above prevent a simple rigorous proof of their non-perturbative existence.…”

Extending Precision Perturbative QCD with Track Functions

“…These correlation functions can be computed in perturbation theory, and are known explicitly for the two [29,[31][32][33][34][35] and threepoint correlator [36]. They have recently received extensive theoretical interest from a variety of communities [27][28][29][30][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53]. In this Letter we will emphasize another remarkable feature of these observables, namely their simple interplay with non-perturbative track functions.…”

Quantum Interference in Jet Substructure from Spinning Gluons

“…), describes the behavior of local operators as they are brought together, in the limit of interest in jet substructure where the light-ray operators E(n) become collinear, there exists a recently developed light-ray OPE [9,12,17,37,38]…”

“…, where the O i (n) are nonlocal light-ray operators [9,12,[39][40][41][42]. However, the use of the light-ray OPE has so far been restricted to conformal field theories (CFTs) [9,17,37,38].…”

“…Transverse spin can also be studied using the twopoint correlator with a polarized source [38]. However, for a source coupling to quarks, polarization effects appear first at O(α 2 s ).…”