Transverse spin in the light-ray OPE

Chang, Cyuan-Han; Koloğlu, Murat; Kravchuk, Petr; Simmons-Duffin, David; Zhiboedov, Alexander

doi:10.1007/jhep05(2022)059

Transverse spin in the light-ray OPE

Journal Article · Tue May 10 00:00:00 EDT 2022 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep05(2022)059· OSTI ID:1879860

Chang, Cyuan-Han ^[1]; Koloğlu, Murat ^[2]; ^[3]; Simmons-Duffin, David ^[4]; Zhiboedov, Alexander ^[5]

California Institute of Technology (CalTech), Pasadena, CA (United States); Institute for Advanced Study
Univ. of Oxford (United Kingdom)
Institute for Advanced Study, Princeton, NJ (United States)
California Institute of Technology (CalTech), Pasadena, CA (United States)
European Organization for Nuclear Research (CERN), Geneva (Switzerland)

We study a product of null-integrated local operators O₁ and O₂ 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 J₁ + J₂ – 1. The terms with higher transverse spin are primary descendants of light-ray operators with higher spins J₁ + J₂ – 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.

View Accepted Manuscript (DOE)

Research Organization:: Institute for Advanced Study, Princeton, NJ (United States)

Sponsoring Organization:: Simons Foundation; USDOE Office of Science (SC)

Grant/Contract Number:: SC0009988; SC0019085

OSTI ID:: 1879860

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 5 Vol. 2022; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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