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Published July 2018 | Version Published + Submitted
Journal Article Open

A spacetime derivation of the Lorentzian OPE inversion formula

Creators

  • 1. ROR icon California Institute of Technology
  • 2. ROR icon Institute for Advanced Study

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.

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.

Attached Files

Published - Simmons-Duffin2018_Article_ASpacetimeDerivationOfTheLoren.pdf

Submitted - 1711.03816

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Simmons-Duffin2018_Article_ASpacetimeDerivationOfTheLoren.pdf

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Additional details

Identifiers

Eprint ID
87817
Resolver ID
CaltechAUTHORS:20180713-090329998

Related works

Describes
http://arxiv.org/abs/1711.03816 (URL)

Funding

Simons Foundation
385600
Simons Foundation
488657
NSF
PHY-1606531
SCOAP3

Dates

Created
2018-07-13
Created from EPrint's datestamp field
Updated
2021-11-15
Created from EPrint's last_modified field

Caltech Custom Metadata

Caltech groups
Walter Burke Institute for Theoretical Physics , Physics Department