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Title: Light-ray operators in conformal field theory

Journal Article · · Journal of High Energy Physics (Online)
ORCiD logo [1];  [1]
  1. California Institute of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
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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.

Research Organization:
California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC); Simons Foundation
Grant/Contract Number:
SC0011632; 488657
OSTI ID:
1611637
Journal Information:
Journal of High Energy Physics (Online), Vol. 2018, Issue 11; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 151 works
Citation information provided by
Web of Science

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Cited By (9)

The analytic functional bootstrap. Part II. Natural bases for the crossing equation journal February 2019
Implications of ANEC for SCFTs in four dimensions journal January 2020
Bootstrapping the long-range Ising model in three dimensions journal January 2019
All Tree-Level Correlators in AdS${}_5\times$S${}_5$ Supergravity: Hidden Ten-Dimensional Conformal Symmetry text January 2018
Bootstrapping the long-range Ising model in three dimensions text January 2018
Quantum Regge Trajectories and the Virasoro Analytic Bootstrap text January 2018
Recursion Relations in Witten Diagrams and Conformal Partial Waves text January 2018
A Crossing-Symmetric OPE Inversion Formula text January 2018
Closed-form expression for cross-channel conformal blocks near the lightcone text January 2019

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Physics
Conformal Field Theory
Field Theories in Higher Dimensions
Conformal and W Symmetry