skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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]
+ Show Author Affiliations
  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.
Copy to clipboard
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
Copy to clipboard
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.
Copy to clipboard
@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}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI:  https://doi.org/10.1007/JHEP07(2018)085
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Citation Metrics:
Cited by: 58 works
Citation information provided by
Web of Science
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

Crossing symmetry in alpha space
journal, November 2017

  • Hogervorst, Matthijs; van Rees, Balt C.
  • Journal of High Energy Physics, Vol. 2017, Issue 11
  • DOI: 10.1007/JHEP11(2017)193

Analyticity in spin in conformal theories
journal, September 2017

More on supersymmetric and 2d analogs of the SYK model
journal, August 2017

  • Murugan, Jeff; Stanford, Douglas; Witten, Edward
  • Journal of High Energy Physics, Vol. 2017, Issue 8
  • DOI: 10.1007/JHEP08(2017)146

Looking for a bulk point
journal, January 2017

  • Maldacena, Juan; Simmons-Duffin, David; Zhiboedov, Alexander
  • Journal of High Energy Physics, Vol. 2017, Issue 1
  • DOI: 10.1007/JHEP01(2017)013

Projectors, shadows, and conformal blocks
journal, April 2014

Averaged null energy condition from causality
journal, July 2017

  • Hartman, Thomas; Kundu, Sandipan; Tajdini, Amirhossein
  • Journal of High Energy Physics, Vol. 2017, Issue 7
  • DOI: 10.1007/JHEP07(2017)066

A note on the SYK model with complex fermions
journal, December 2017

A bound on chaos
journal, August 2016

  • Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas
  • Journal of High Energy Physics, Vol. 2016, Issue 8
  • DOI: 10.1007/JHEP08(2016)106

Eikonal approximation in AdS/CFT: Conformal partial waves and finite N four-point functions
journal, April 2007

Conformal Regge theory
journal, December 2012

  • Costa, Miguel S.; Goncalves, Vasco; Penedones, João
  • Journal of High Energy Physics, Vol. 2012, Issue 12
  • DOI: 10.1007/JHEP12(2012)091

Convexity and liberation at large spin
journal, November 2013

  • Komargodski, Zohar; Zhiboedov, Alexander
  • Journal of High Energy Physics, Vol. 2013, Issue 11
  • DOI: 10.1007/JHEP11(2013)140

The analytic bootstrap and AdS superhorizon locality
journal, December 2013

  • Fitzpatrick, A. Liam; Kaplan, Jared; Poland, David
  • Journal of High Energy Physics, Vol. 2013, Issue 12
  • DOI: 10.1007/JHEP12(2013)004

Conformal bootstrap with slightly broken higher spin symmetry
journal, June 2016

  • Alday, Luis F.; Zhiboedov, Alexander
  • Journal of High Energy Physics, Vol. 2016, Issue 6
  • DOI: 10.1007/JHEP06(2016)091

An algebraic approach to the analytic bootstrap
journal, April 2017

  • Alday, Luis F.; Zhiboedov, Alexander
  • Journal of High Energy Physics, Vol. 2017, Issue 4
  • DOI: 10.1007/JHEP04(2017)157

Analytic bootstrap at large spin
journal, November 2015

  • Kaviraj, Apratim; Sen, Kallol; Sinha, Aninda
  • Journal of High Energy Physics, Vol. 2015, Issue 11
  • DOI: 10.1007/JHEP11(2015)083

Large Spin Perturbation Theory for Conformal Field Theories
journal, September 2017

The lightcone bootstrap and the spectrum of the 3d Ising CFT
journal, March 2017

Simplifying large spin bootstrap in Mellin space
journal, January 2018

  • Dey, Parijat; Ghosh, Kausik; Sinha, Aninda
  • Journal of High Energy Physics, Vol. 2018, Issue 1
  • DOI: 10.1007/JHEP01(2018)152

Positivity constraints for anomalous dimensions
journal, October 1973

Bounds for OPE coefficients on the Regge trajectory
journal, October 2017

  • Costa, Miguel S.; Hansen, Tobias; Penedones, João
  • Journal of High Energy Physics, Vol. 2017, Issue 10
  • DOI: 10.1007/JHEP10(2017)197

Weight shifting operators and conformal blocks
journal, February 2018

  • Karateev, Denis; Kravchuk, Petr; Simmons-Duffin, David
  • Journal of High Energy Physics, Vol. 2018, Issue 2
  • DOI: 10.1007/JHEP02(2018)081

Casimir recursion relations for general conformal blocks
journal, February 2018

Conformal four point functions and the operator product expansion
journal, April 2001

Bootstrapping mixed correlators in the 3D Ising model
journal, November 2014

  • Kos, Filip; Poland, David; Simmons-Duffin, David
  • Journal of High Energy Physics, Vol. 2014, Issue 11
  • DOI: 10.1007/JHEP11(2014)109

Recursion relations for conformal blocks
journal, September 2016

  • Penedones, João; Trevisani, Emilio; Yamazaki, Masahito
  • Journal of High Energy Physics, Vol. 2016, Issue 9
  • DOI: 10.1007/JHEP09(2016)070

On analytic properties of vertex parts in quantum field theory
journal, October 1959

Singularities in the physical region
journal, July 1965

Singularities and Discontinuities of Feynman Amplitudes
journal, September 1960

  • Cutkosky, R. E.
  • Journal of Mathematical Physics, Vol. 1, Issue 5
  • DOI: 10.1063/1.1703676

Causality constraints in conformal field theory
journal, May 2016

  • Hartman, Thomas; Jain, Sachin; Kundu, Sandipan
  • Journal of High Energy Physics, Vol. 2016, Issue 5
  • DOI: 10.1007/JHEP05(2016)099
    [ × clear filter / sort ]

    Works referencing / citing this record:

    Higher spin ANEC and the space of CFTs
    journal, July 2019

    A study of quantum field theories in AdS at finite coupling
    journal, January 2019

    • Carmi, Dean; Di Pietro, Lorenzo; Komatsu, Shota
    • Journal of High Energy Physics, Vol. 2019, Issue 1
    • DOI: 10.1007/jhep01(2019)200

    Null infinity and unitary representation of the Poincare group
    journal, January 2019

    Thermal CFTs in momentum space
    journal, January 2020

    Closed-form expression for cross-channel conformal blocks near the lightcone
    journal, January 2020

    Multipoint conformal blocks in the comb channel
    journal, February 2019

    Hints of unitarity at large N in the O(N )3 tensor field theory
    journal, February 2020

    • Benedetti, Dario; Gurau, Razvan; Harribey, Sabine
    • Journal of High Energy Physics, Vol. 2020, Issue 2
    • DOI: 10.1007/jhep02(2020)072

    Recursion relations in Witten diagrams and conformal partial waves
    journal, May 2019

    Quantum Regge trajectories and the Virasoro analytic bootstrap
    journal, May 2019

    • Collier, Scott; Gobeil, Yan; Maxfield, Henry
    • Journal of High Energy Physics, Vol. 2019, Issue 5
    • DOI: 10.1007/jhep05(2019)212

    Genus-one string amplitudes from conformal field theory
    journal, June 2019

    • Alday, Luis F.; Bissi, Agnese; Perlmutter, Eric
    • Journal of High Energy Physics, Vol. 2019, Issue 6
    • DOI: 10.1007/jhep06(2019)010

    Scalar-fermion analytic bootstrap in 4D
    journal, June 2019

    • Elkhidir, Emtinan; Karateev, Denis
    • Journal of High Energy Physics, Vol. 2019, Issue 6
    • DOI: 10.1007/jhep06(2019)026

    Generalized fishnets and exact four-point correlators in chiral CFT4
    journal, June 2019

    • Kazakov, Vladimir; Olivucci, Enrico; Preti, Michelangelo
    • Journal of High Energy Physics, Vol. 2019, Issue 6
    • DOI: 10.1007/jhep06(2019)078

    A crossing-symmetric OPE inversion formula
    journal, June 2019

    Fermion conformal bootstrap in 4d
    journal, June 2019

    • Karateev, Denis; Kravchuk, Petr; Serone, Marco
    • Journal of High Energy Physics, Vol. 2019, Issue 6
    • DOI: 10.1007/jhep06(2019)088

    Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory
    journal, July 2018

    • Isachenkov, Mikhail; Schomerus, Volker
    • Journal of High Energy Physics, Vol. 2018, Issue 7
    • DOI: 10.1007/jhep07(2018)180

    Large N renormalization group flows in 3d $$ \mathcal{N} $$ = 1 Chern-Simons-Matter theories
    journal, July 2019

    Exact correlation functions in conformal fishnet theory
    journal, August 2019

    • Gromov, Nikolay; Kazakov, Vladimir; Korchemsky, Gregory
    • Journal of High Energy Physics, Vol. 2019, Issue 8
    • DOI: 10.1007/jhep08(2019)123

    Scalar CFTs and their large N limits
    journal, September 2018

    Veneziano amplitude of Vasiliev theory
    journal, October 2018

    • Turiaci, Gustavo J.; Zhiboedov, Alexander
    • Journal of High Energy Physics, Vol. 2018, Issue 10
    • DOI: 10.1007/jhep10(2018)034

    The conformal bootstrap at finite temperature
    journal, October 2018

    • Iliesiu, Luca; Koloğlu, Murat; Mahajan, Raghu
    • Journal of High Energy Physics, Vol. 2018, Issue 10
    • DOI: 10.1007/jhep10(2018)070

    Momentum-space conformal blocks on the light cone
    journal, October 2018

    Celestial amplitudes: conformal partial waves and soft limits
    journal, October 2019

    • Nandan, Dhritiman; Schreiber, Anders; Volovich, Anastasia
    • Journal of High Energy Physics, Vol. 2019, Issue 10
    • DOI: 10.1007/jhep10(2019)018

    Harmonic analysis and mean field theory
    journal, October 2019

    • Karateev, Denis; Kravchuk, Petr; Simmons-Duffin, David
    • Journal of High Energy Physics, Vol. 2019, Issue 10
    • DOI: 10.1007/jhep10(2019)217

    Analytic Euclidean bootstrap
    journal, October 2019

    • Mukhametzhanov, Baur; Zhiboedov, Alexander
    • Journal of High Energy Physics, Vol. 2019, Issue 10
    • DOI: 10.1007/jhep10(2019)270

    Light-ray operators in conformal field theory
    journal, November 2018

    • Kravchuk, Petr; Simmons-Duffin, David
    • Journal of High Energy Physics, Vol. 2018, Issue 11
    • DOI: 10.1007/jhep11(2018)102

    Bootstrapping the minimal 3D SCFT
    journal, November 2018

    • Atanasov, Alexander; Hillman, Aaron; Poland, David
    • Journal of High Energy Physics, Vol. 2018, Issue 11
    • DOI: 10.1007/jhep11(2018)140

    R-current three-point functions in 4d N$$ \mathcal{N} $$ = 1 superconformal theories
    journal, December 2018

    • Manenti, Andrea; Stergiou, Andreas; Vichi, Alessandro
    • Journal of High Energy Physics, Vol. 2018, Issue 12
    • DOI: 10.1007/jhep12(2018)108

    Quantum corrections to the BTZ black hole extremality bound from the conformal bootstrap
    journal, December 2019

    Critical O( N ) model to order ϵ 4 from analytic bootstrap
    journal, December 2018

    • Henriksson, Johan; van Loon, Mark
    • Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 2
    • DOI: 10.1088/1751-8121/aaf1e2

    Universality at large transverse spin in defect CFT
    text, January 2018

    • Lemos, Madalena; Liendo, Pedro; Meineri, Marco
    • Deutsches Elektronen-Synchrotron, DESY, Hamburg
    • DOI: 10.3204/pubdb-2018-03901
      [ × clear filter / sort ]

      Similar Records in DOE PAGES and OSTI.GOV collections: