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

Title: Landau diagrams in AdS and S-matrices from conformal correlators

Abstract

Quantum field theories in AdS generate conformal correlation functions on the boundary, and in the limit where AdS is nearly flat one should be able to extract an S-matrix from such correlators. We discuss a particularly simple position-space procedure to do so. It features a direct map from boundary positions to (on-shell) momenta and thereby relates cross ratios to Mandelstam invariants. This recipe succeeds in several examples, includes the momentum-conserving delta functions, and can be shown to imply the two proposals in based on Mellin space and on the OPE data. Interestingly the procedure does not always work: the Landau singularities of a Feynman diagram are shown to be part of larger regions, to be called ‘bad regions’, where the flat-space limit of the Witten diagram diverges. To capture these divergences we introduce the notion of Landau diagrams in AdS. As in flat space, these describe on-shell particles propagating over large distances in a complexified space, with a form of momentum conservation holding at each bulk vertex. As an application we recover the anomalous threshold of the four-point triangle diagram at the boundary of a bad region.

Authors:
 [1];  [2];  [3];  [3]
  1. Inst. for Advanced Study, Princeton, NJ (United States)
  2. Sorbonne Univ., Paris Cedex (France)
  3. Ecole Polytechnique, Palaiseau (France)
Publication Date:
Research Org.:
Institute for Advanced Study, Princeton, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1737770
Grant/Contract Number:  
SC0009988
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: 2020; Journal Issue: 11; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdS-CFT Correspondence; Conformal Field Theory; Field Theories in Higher Dimensions; Scattering Amplitudes

Citation Formats

Komatsu, Shota, Paulos, Miguel F., van Rees, Balt C., and Zhao, Xiang. Landau diagrams in AdS and S-matrices from conformal correlators. United States: N. p., 2020. Web. https://doi.org/10.1007/jhep11(2020)046.
Komatsu, Shota, Paulos, Miguel F., van Rees, Balt C., & Zhao, Xiang. Landau diagrams in AdS and S-matrices from conformal correlators. United States. https://doi.org/10.1007/jhep11(2020)046
Komatsu, Shota, Paulos, Miguel F., van Rees, Balt C., and Zhao, Xiang. Tue . "Landau diagrams in AdS and S-matrices from conformal correlators". United States. https://doi.org/10.1007/jhep11(2020)046. https://www.osti.gov/servlets/purl/1737770.
@article{osti_1737770,
title = {Landau diagrams in AdS and S-matrices from conformal correlators},
author = {Komatsu, Shota and Paulos, Miguel F. and van Rees, Balt C. and Zhao, Xiang},
abstractNote = {Quantum field theories in AdS generate conformal correlation functions on the boundary, and in the limit where AdS is nearly flat one should be able to extract an S-matrix from such correlators. We discuss a particularly simple position-space procedure to do so. It features a direct map from boundary positions to (on-shell) momenta and thereby relates cross ratios to Mandelstam invariants. This recipe succeeds in several examples, includes the momentum-conserving delta functions, and can be shown to imply the two proposals in based on Mellin space and on the OPE data. Interestingly the procedure does not always work: the Landau singularities of a Feynman diagram are shown to be part of larger regions, to be called ‘bad regions’, where the flat-space limit of the Witten diagram diverges. To capture these divergences we introduce the notion of Landau diagrams in AdS. As in flat space, these describe on-shell particles propagating over large distances in a complexified space, with a form of momentum conservation holding at each bulk vertex. As an application we recover the anomalous threshold of the four-point triangle diagram at the boundary of a bad region.},
doi = {10.1007/jhep11(2020)046},
journal = {Journal of High Energy Physics (Online)},
number = 11,
volume = 2020,
place = {United States},
year = {2020},
month = {11}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Save / Share:

Works referenced in this record:

Four point function of N = 4 $$ \mathcal{N}=4 $$ stress-tensor multiplet at strong coupling
journal, April 2015


Boundary correlators in WZW model on AdS2
journal, May 2020

  • Beccaria, Matteo; Jiang, Hongliang; Tseytlin, Arkady A.
  • Journal of High Energy Physics, Vol. 2020, Issue 5
  • DOI: 10.1007/JHEP05(2020)099

On boundary correlators in Liouville theory on AdS2
journal, July 2019

  • Beccaria, Matteo; Tseytlin, Arkady A.
  • Journal of High Energy Physics, Vol. 2019, Issue 7
  • DOI: 10.1007/JHEP07(2019)008

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


Singularities in the physical region
journal, July 1965


Writing CFT correlation functions as AdS scattering amplitudes
journal, March 2011


A conformal dispersion relation: correlations from absorption
journal, September 2020


Rigid holography and six-dimensional N = 2 0 $$ \mathcal{N}=\left(2,0\right) $$ theories on AdS5 × S $$ \mathbb{S} $$ 1
journal, March 2015

  • Aharony, Ofer; Berkooz, Micha; Rey, Soo-Jong
  • Journal of High Energy Physics, Vol. 2015, Issue 3
  • DOI: 10.1007/JHEP03(2015)121

Half-BPS Wilson loop and AdS 2 /CFT 1
journal, September 2017


Flat space physics from AdS/CFT
journal, July 2019


A natural language for AdS/CFT correlators
journal, November 2011

  • Fitzpatrick, A. Liam; Kaplan, Jared; Penedones, Joao
  • Journal of High Energy Physics, Vol. 2011, Issue 11
  • DOI: 10.1007/JHEP11(2011)095

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

Radial coordinates for conformal blocks
journal, May 2013


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

String theory beyond the Planck scale
journal, July 1988


Real-time gauge/gravity duality: prescription, renormalization and examples
journal, May 2009


Real-Time Gauge/Gravity Duality
journal, August 2008


Asymptotic fragility, near AdS2 holography and T T ¯ $$ T\overline{T} $$
journal, September 2017

  • Dubovsky, Sergei; Gorbenko, Victor; Mirbabayi, Mehrdad
  • Journal of High Energy Physics, Vol. 2017, Issue 9
  • DOI: 10.1007/JHEP09(2017)136

BMS supertranslations and Weinberg’s soft graviton theorem
journal, May 2015

  • He, Temple; Lysov, Vyacheslav; Mitra, Prahar
  • Journal of High Energy Physics, Vol. 2015, Issue 5
  • DOI: 10.1007/JHEP05(2015)151

Nonperturbative Mellin amplitudes: existence, properties, applications
journal, August 2020

  • Penedones, Joao; Silva, Joao A.; Zhiboedov, Alexander
  • Journal of High Energy Physics, Vol. 2020, Issue 8
  • DOI: 10.1007/JHEP08(2020)031

Holographic three-point functions for short operators
journal, July 2012


The S-matrix bootstrap II: two dimensional amplitudes
journal, November 2017

  • Paulos, Miguel F.; Penedones, Joao; Toledo, Jonathan
  • Journal of High Energy Physics, Vol. 2017, Issue 11
  • DOI: 10.1007/JHEP11(2017)143

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

The S-matrix bootstrap IV: multiple amplitudes
journal, November 2019

  • Homrich, Alexandre; Penedones, João; Toledo, Jonathan
  • Journal of High Energy Physics, Vol. 2019, Issue 11
  • DOI: 10.1007/JHEP11(2019)076

Analyticity in spin in conformal theories
journal, September 2017


Lecture notes on holographic renormalization
journal, November 2002


Infrared Photons and Gravitons
journal, October 1965


Witten diagrams revisited: the AdS geometry of conformal blocks
journal, January 2016

  • Hijano, Eliot; Kraus, Per; Perlmutter, Eric
  • Journal of High Energy Physics, Vol. 2016, Issue 1
  • DOI: 10.1007/JHEP01(2016)146

Confinement in anti-de Sitter space
journal, February 2013

  • Aharony, Ofer; Berkooz, Micha; Tong, David
  • Journal of High Energy Physics, Vol. 2013, Issue 2
  • DOI: 10.1007/JHEP02(2013)076

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

Froissart bound for/from CFT Mellin amplitudes
journal, January 2020


The S-matrix bootstrap. Part I: QFT in AdS
journal, November 2017

  • Paulos, Miguel F.; Penedones, Joao; Toledo, Jonathan
  • Journal of High Energy Physics, Vol. 2017, Issue 11
  • DOI: 10.1007/JHEP11(2017)133

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


Conformal partial waves and the operator product expansion
journal, February 2004


Towards Feynman rules for Mellin amplitudes in AdS/CFT
journal, October 2011


Non-abelian Toda theory on AdS2 and $$ {\mathrm{AdS}}_2/{\mathrm{CFT}}_2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} $$ duality
journal, September 2019

  • Beccaria, Matteo; Jiang, Hongliang; Tseytlin, Arkady A.
  • Journal of High Energy Physics, Vol. 2019, Issue 9
  • DOI: 10.1007/s13130-019-11219-y