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Light-ray operators in conformal field theory

Kravchuk, Petr and Simmons-Duffin, David (2018) Light-ray operators in conformal field theory. Journal of High Energy Physics, 2018 (11). Art. No. 102. ISSN 1126-6708. http://resolver.caltech.edu/CaltechAUTHORS:20181121-100428583

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/JHEP11(2018)102DOIArticle
https://arxiv.org/abs/1805.00098arXivDiscussion Paper
ORCID:
AuthorORCID
Kravchuk, Petr0000-0003-0977-3686
Simmons-Duffin, David0000-0002-2937-9515
Additional Information:© 2018 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: September 24, 2018; Accepted: October 22, 2018; Published: November 19, 2018. We thank Clay Córdova, Thomas Dumitrescu, Abhijit Gadde, Luca Iliesiu, Daniel Jafferis, Alexei Kitaev, Murat Koloğlu, Raghu Mahajan, Eric Perlmutter, Matt Strassler, and Aron Wall for helpful discussions. We thank Simon Caron-Huot, Tom Hartman, Denis Karateev, Juan Maldacena, Douglas Stanford, and Sasha Zhiboedov for discussions and comments on the draft. DSD is supported by Simons Foundation grant 488657 (Simons Collaboration on the Nonperturbative Bootstrap). This work was supported by DOE grant DE-SC0011632 and the Walter Burke Institute for Theoretical Physics.
Group:Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
Simons Foundation488657
Department of Energy (DOE)DE-SC0011632
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
SCOAP3UNSPECIFIED
Subject Keywords:Conformal Field Theory; Field Theories in Higher Dimensions; Conformal and W Symmetry
Record Number:CaltechAUTHORS:20181121-100428583
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20181121-100428583
Official Citation:Kravchuk, P. & Simmons-Duffin, D. J. High Energ. Phys. (2018) 2018: 102. https://doi.org/10.1007/JHEP11(2018)102
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91132
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:21 Nov 2018 18:13
Last Modified:21 Nov 2018 18:13

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