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A spacetime derivation of the Lorentzian OPE inversion formula

Simmons-Duffin, David and Stanford, Douglas and Witten, Edward (2018) A spacetime derivation of the Lorentzian OPE inversion formula. Journal of High Energy Physics, 2018 (7). Art. No. 85. ISSN 1126-6708. https://resolver.caltech.edu/CaltechAUTHORS:20180713-090329998

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Abstract

Caron-Huot has recently given an interesting formula that determines OPE data in a conformal field theory in terms of a weighted integral of the four-point function over a Lorentzian region of cross-ratio space. We give a new derivation of this formula based on Wick rotation in spacetime rather than cross-ratio space. The derivation is simple in two dimensions but more involved in higher dimensions. We also derive a Lorentzian inversion formula in one dimension that sheds light on previous observations about the chaos regime in the SYK model.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/JHEP07(2018)085DOIArticle
http://arxiv.org/abs/1711.03816arXivDiscussion Paper
ORCID:
AuthorORCID
Simmons-Duffin, David0000-0002-2937-9515
Witten, Edward0000-0002-7752-6073
Additional Information:© The Author(s) 2018. 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. First Online: 12 July 2018. Article funded by SCOAP3. We thank Simon Caron-Huot, Abhijit Gadde, Denis Karateev, Petr Kravchuk, Eric Perlmutter, and Shu-Heng Shao for discussions. DS is supported by Simons Foundation grant 385600. DSD is supported by Simons Foundation grant 488657. EW is supported in part by NSF Grant PHY-1606531.
Group:Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
Simons Foundation385600
Simons Foundation488657
NSFPHY-1606531
SCOAP3UNSPECIFIED
Subject Keywords:Conformal and W Symmetry, Conformal Field Theory
Issue or Number:7
Record Number:CaltechAUTHORS:20180713-090329998
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180713-090329998
Official Citation:Simmons-Duffin, D., Stanford, D. & Witten, E. J. High Energ. Phys. (2018) 2018: 85. https://doi.org/10.1007/JHEP07(2018)085
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:87817
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:13 Jul 2018 17:20
Last Modified:03 Oct 2019 20:00

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