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Article
Report number	arXiv:2010.04726 ; CALT-TH 2020-039 ; CERN-TH-2020-164
Title	Transverse spin in the light-ray OPE
Author(s)	Chang, Cyuan-Han (Caltech, Pasadena (main)) ; Kologlu, Murat (Oxford U., Inst. Math.) ; Kravchuk, Petr (Princeton, Inst. Advanced Study) ; Simmons-Duffin, David (Caltech, Pasadena (main)) ; Zhiboedov, Alexander (CERN)
Publication	2022-05-10
Imprint	2020-10-09
Number of pages	100
Note	71 pages + appendices
In:	JHEP 2205 (2022) 059
DOI	10.1007/JHEP05(2022)059
Subject category	hep-th ; Particle Physics - Theory
Abstract	We study a product of null-integrated local operators $\mathcal{O}_1$ and $\mathcal{O}_2$ 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 $\mathcal{N}=4$ SYM, finding perfect agreement.
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