Light-ray operators in conformal field theory
- Creators
- Kravchuk, Petr
- Simmons-Duffin, David
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.
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.Attached Files
Published - Kravchuk-Simmons-Duffin2018_Article_Light-rayOperatorsInConformalF.pdf
Submitted - 1805.00098.pdf
Files
Name | Size | Download all |
---|---|---|
md5:d5918839dc1527b01594c71951da3ad4
|
1.7 MB | Preview Download |
md5:fc97c51c9cfa79b56974951e0ebc3236
|
1.1 MB | Preview Download |
Additional details
- Eprint ID
- 91132
- Resolver ID
- CaltechAUTHORS:20181121-100428583
- 488657
- Simons Foundation
- DE-SC0011632
- Department of Energy (DOE)
- Walter Burke Institute for Theoretical Physics, Caltech
- SCOAP3
- Created
-
2018-11-21Created from EPrint's datestamp field
- Updated
-
2021-11-16Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics