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Light-ray operators in conformal field theory

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2]
  1. California Institute of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics; DOE/OSTI
  2. 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:
Simons Foundation; USDOE Office of Science (SC)
Grant/Contract Number:
SC0011632
OSTI ID:
1611637
Journal Information:
Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 11 Vol. 2018; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (24)

All tree-level correlators in AdS5×S5 supergravity: hidden ten-dimensional conformal symmetry journal January 2019
Closed-form expression for cross-channel conformal blocks near the lightcone journal January 2020
Implications of ANEC for SCFTs in four dimensions journal January 2020
Chaos in the butterfly cone journal January 2020
The analytic functional bootstrap. Part II. Natural bases for the crossing equation journal February 2019
A bound on massive higher spin particles journal April 2019
Recursion relations in Witten diagrams and conformal partial waves journal May 2019
Quantum Regge trajectories and the Virasoro analytic bootstrap journal May 2019
A crossing-symmetric OPE inversion formula journal June 2019
Fermion conformal bootstrap in 4d journal June 2019
Higher spin ANEC and the space of CFTs journal July 2019
Einstein gravity from ANEC correlators journal August 2019
Harmonic analysis and mean field theory journal October 2019
Probing universalities in d > 2 CFTs: from black holes to shockwaves journal November 2019
Quantum corrections to the BTZ black hole extremality bound from the conformal bootstrap journal December 2019
Sphere packing and quantum gravity journal December 2019
Bootstrapping the long-range Ising model in three dimensions journal January 2019
Collinear limit of the energy-energy correlator journal July 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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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Conformal Field Theory
Conformal and W Symmetry
Field Theories in Higher Dimensions
Physics