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Title: A spacetime derivation of the Lorentzian OPE inversion formula

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.

Authors:
 [1];  [2];  [2]
  1. California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics; Inst. for Advanced Study, Princeton, NJ (United States)
  2. Inst. for Advanced Study, Princeton, NJ (United States)
Publication Date:
Research Org.:
Institute for Advanced Study, Princeton, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC); Simons Foundation; National Science Foundation (NSF)
OSTI Identifier:
1598252
Grant/Contract Number:  
SC0009988; 385600; 488657; PHY-1606531
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 7; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; field theory: conformal; dimension: 2; dimension: 1; n-point function: 4; operator product expansion; space-time; higher-dimensional; rotation; chaos; conformal field theory; conformal and W symmetry

Citation Formats

Simmons-Duffin, David, Stanford, Douglas, and Witten, Edward. A spacetime derivation of the Lorentzian OPE inversion formula. United States: N. p., 2018. Web. doi:10.1007/JHEP07(2018)085.
Simmons-Duffin, David, Stanford, Douglas, & Witten, Edward. A spacetime derivation of the Lorentzian OPE inversion formula. United States. doi:https://doi.org/10.1007/JHEP07(2018)085
Simmons-Duffin, David, Stanford, Douglas, and Witten, Edward. Thu . "A spacetime derivation of the Lorentzian OPE inversion formula". United States. doi:https://doi.org/10.1007/JHEP07(2018)085. https://www.osti.gov/servlets/purl/1598252.
@article{osti_1598252,
title = {A spacetime derivation of the Lorentzian OPE inversion formula},
author = {Simmons-Duffin, David and Stanford, Douglas and Witten, Edward},
abstractNote = {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.},
doi = {10.1007/JHEP07(2018)085},
journal = {Journal of High Energy Physics (Online)},
number = 7,
volume = 2018,
place = {United States},
year = {2018},
month = {7}
}

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Cited by: 58 works
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