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Title: Light-ray operators in conformal field theory

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.

Authors:
ORCiD logo [1];  [1]
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  1. California Institute of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
Publication Date:
Research Org.:
California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC); Simons Foundation
OSTI Identifier:
1611637
Grant/Contract Number:  
SC0011632; 488657
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 11; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics; Conformal Field Theory; Field Theories in Higher Dimensions; Conformal and W Symmetry

Citation Formats

Kravchuk, Petr, and Simmons-Duffin, David. Light-ray operators in conformal field theory. United States: N. p., 2018. Web. doi:10.1007/jhep11(2018)102.
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Kravchuk, Petr, & Simmons-Duffin, David. Light-ray operators in conformal field theory. United States. https://doi.org/10.1007/jhep11(2018)102
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Kravchuk, Petr, and Simmons-Duffin, David. Mon . "Light-ray operators in conformal field theory". United States. https://doi.org/10.1007/jhep11(2018)102. https://www.osti.gov/servlets/purl/1611637.
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@article{osti_1611637,
title = {Light-ray operators in conformal field theory},
author = {Kravchuk, Petr and Simmons-Duffin, David},
abstractNote = {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.},
doi = {10.1007/jhep11(2018)102},
journal = {Journal of High Energy Physics (Online)},
number = 11,
volume = 2018,
place = {United States},
year = {Mon Nov 19 00:00:00 EST 2018},
month = {Mon Nov 19 00:00:00 EST 2018}
}
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https://doi.org/10.1007/jhep11(2018)102
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  • DOI: 10.2307/1968455
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