Gluing Ladder Feynman Diagrams into Fishnets

Basso, Benjamin; Dixon, Lance J.

doi:10.1103/PhysRevLett.119.071601

Title: Gluing Ladder Feynman Diagrams into Fishnets

Abstract

We use integrability at weak coupling to compute fishnet diagrams for four-point correlation functions in planar Φ ⁴ theory. Our results are always multilinear combinations of ladder integrals, which are in turn built out of classical polylogarithms. The Steinmann relations provide a powerful constraint on such linear combinations, which leads to a natural conjecture for any fishnet diagram as the determinant of a matrix of ladder integrals.

Authors:

Basso, Benjamin ^[1]; Dixon, Lance J. ^[2]

PSL Research Univ., Paris (France)
SLAC National Accelerator Lab., Menlo Park, CA (United States); Stanford Univ., CA (United States); Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics

Publication Date:: Mon Aug 14 00:00:00 EDT 2017

Research Org.:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Org.:: USDOE; National Science Foundation (NSF)

OSTI Identifier:: 1389318

Alternate Identifier(s):: OSTI ID: 1375051

Report Number(s):: SLAC-PUB-16967
Journal ID: ISSN 0031-9007; PRLTAO; TRN: US1702819

Grant/Contract Number:: AC02–76SF00515; NSF PHY-1125915

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Volume: 119; Journal Issue: 7; Journal ID: ISSN 0031-9007

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Basso, Benjamin, and Dixon, Lance J. Gluing Ladder Feynman Diagrams into Fishnets.  United States: N. p., 2017. 
Web.  doi:10.1103/PhysRevLett.119.071601.

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                    Basso, Benjamin, & Dixon, Lance J. Gluing Ladder Feynman Diagrams into Fishnets.  United States.  https://doi.org/10.1103/PhysRevLett.119.071601

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                    Basso, Benjamin, and Dixon, Lance J. Mon .  
"Gluing Ladder Feynman Diagrams into Fishnets".  United States.  https://doi.org/10.1103/PhysRevLett.119.071601.  https://www.osti.gov/servlets/purl/1389318.

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@article{osti_1389318,

  title        = {Gluing Ladder Feynman Diagrams into Fishnets},

  author       = {Basso, Benjamin and Dixon, Lance J.},

  abstractNote = {We use integrability at weak coupling to compute fishnet diagrams for four-point correlation functions in planar Φ 4 theory. Our results are always multilinear combinations of ladder integrals, which are in turn built out of classical polylogarithms. The Steinmann relations provide a powerful constraint on such linear combinations, which leads to a natural conjecture for any fishnet diagram as the determinant of a matrix of ladder integrals.},

  doi          = {10.1103/PhysRevLett.119.071601},

  journal      = {Physical Review Letters},

  number       = 7,

  volume       = 119,

  place        = {United States},

  year         = {Mon Aug 14 00:00:00 EDT 2017},

  month        = {Mon Aug 14 00:00:00 EDT 2017}

}

Copy to clipboard

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Works referenced in this record:

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Heptagons from the Steinmann Cluster Bootstrap
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arXiv
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Jiang, Yunfeng; Komatsu, Shota; Kostov, Ivan
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Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
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Caron-Huot, Simon; Dixon, Lance J.; McLeod, Andrew
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Hexagonalization of Correlation Functions
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Fleury, Thiago; Komatsu, Shota
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Heptagons from the Steinmann Cluster Bootstrap
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Works referencing / citing this record:

Continuum limit of fishnet graphs and AdS sigma model
journal, January 2019

Basso, Benjamin; Zhong, De-liang
Journal of High Energy Physics, Vol. 2019, Issue 1
DOI: 10.1007/jhep01(2019)002

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

Twistor fishnets
journal, January 2020

Adamo, Tim; Jaitly, Sumer
Journal of Physics A: Mathematical and Theoretical, Vol. 53, Issue 5
DOI: 10.1088/1751-8121/ab5f88

Octagons I: combinatorics and non-planar resummations
other, January 2019

Bargheer, Till; Coronado, Frank; Vieira, Pedro
Berlin; Heidelberg : Springer
DOI: 10.15488/11307

The double pentaladder integral to all ordersC
text, January 2018

Caron-Huot, Simon; Dixon, Lance J.; Von Hippel, Matt
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2018-05437

Numbers and Functions in Quantum Field Theory
text, January 2016

Schnetz, Oliver
arXiv
DOI: 10.48550/arxiv.1606.08598

Yangian Symmetry for Fishnet Feynman Graphs
text, January 2017

Chicherin, Dmitry; Kazakov, Vladimir; Loebbert, Florian
arXiv
DOI: 10.48550/arxiv.1708.00007

The Double Pentaladder Integral to All Orders
text, January 2018

Caron-Huot, Simon; Dixon, Lance J.; von Hippel, Matt
arXiv
DOI: 10.48550/arxiv.1806.01361

Generalized Fishnets and Exact Four-Point Correlators in Chiral CFT$_4$
text, January 2019

Kazakov, Vladimir; Olivucci, Enrico; Preti, Michelangelo
arXiv
DOI: 10.48550/arxiv.1901.00011

Twistor fishnets
text, January 2019

Adamo, Tim; Jaitly, Sumer
arXiv
DOI: 10.48550/arxiv.1908.11220

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Title: Gluing Ladder Feynman Diagrams into Fishnets

Abstract

Citation Formats

Polylogarithmes multiples uniformes en une variable journal, April 2004

Publisher’s Note: New Integrable 4D Quantum Field Theories from Strongly Deformed Planar N = 4 Supersymmetric Yang-Mills Theory [Phys. Rev. Lett. 117 , 201602 (2016)] journal, December 2016

Heptagons from the Steinmann cluster bootstrap journal, February 2017

Space-time S-matrix and flux-tube S-matrix III. The two-particle contributions journal, August 2014

Comments on operators with large spin journal, November 2007

Space-time S-matrix and flux tube S-matrix II. Extracting and matching data journal, January 2014

Asymptotic dispersion relation for the six-particle amplitude journal, October 1982

N=4 supersymmetric Yang–Mills scattering amplitudes at high energies: the Regge cut contribution journal, December 2009

Summation of an infinite series of ladder diagrams journal, June 1993

Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations journal, October 2016

Quantum mechanics of null polygonal Wilson loops journal, May 2014

Quantum spectral curve for arbitrary state/operator in AdS5/CFT4 journal, September 2015

Bootstrapping a Five-Loop Amplitude Using Steinmann Relations journal, December 2016

Strings in flat space and pp waves from Script N = 4 Super Yang Mills journal, April 2002

An operator product expansion for polygonal null Wilson loops journal, April 2011

Hexagonalization of correlation functions journal, January 2017

Optical theorems and steinmann relations journal, April 1975

Review of AdS/CFT Integrability: An Overview journal, October 2011

New Integrable 4D Quantum Field Theories from Strongly Deformed Planar N = 4 Supersymmetric Yang-Mills Theory journal, November 2016

BFKL Pomeron, Reggeized gluons, and Bern-Dixon-Smirnov amplitudes journal, August 2009

A semi-classical limit of the gauge/string correspondence journal, August 2002

Exponential suppression with four legs and an infinity of loops journal, August 2010

Separation of variables for the quantum SL( 2,Bbb R ) spin chain journal, July 2003

Magic identities for conformal four-point integrals journal, January 2007

“Fishing-net” diagrams as a completely integrable system journal, November 1980

A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon journal, March 2015

OPE for all helicity amplitudes II. Form factors and data analysis journal, December 2015

Clustering and the three-point function journal, October 2016

Multi-loop Feynman integrals and conformal quantum mechanics journal, July 2003

Uniqueness of two-loop master contours journal, October 2012

Quantum Spectral Curve for Planar N = 4 Super-Yang-Mills Theory journal, January 2014

Bethe ansätze for GKP strings journal, February 2014

Exact results for three- and four-point ladder diagrams with an arbitrary number of rungs journal, May 1993

Graphical functions and single-valued multiple polylogarithms journal, January 2014

Gluing hexagons at three loops journal, June 2016

Nonsinglet pentagons and NMHV amplitudes journal, July 2015

Bootstrapping the three-loop hexagon journal, November 2011

Spacetime and Flux Tube S -Matrices at Finite Coupling for N = 4 Supersymmetric Yang-Mills Theory journal, August 2013

Graphical functions in parametric space journal, December 2016

Leading singularities and off-shell conformal integrals journal, August 2013

Generalised ladders and single-valued polylogs journal, February 2013

Generalised Ladders and Single-valued Polylogs text, January 2012

Heptagons from the Steinmann Cluster Bootstrap text, January 2017

Leading singularities and off-shell conformal integrals text, January 2013

Quantum mechanics of null polygonal Wilson loops text, January 2014

Quantum mechanics of null polygonal Wilson loops text, January 2014

BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes text, January 2008

N=4 supersymmetric Yang Mills scattering amplitudes at high energies: the Regge cut contribution text, January 2008

An Operator Product Expansion for Polygonal null Wilson Loops text, January 2010

Review of AdS/CFT Integrability: An Overview text, January 2010

Bootstrapping the three-loop hexagon text, January 2011

Uniqueness of two-loop master contours text, January 2012

Graphical functions and single-valued multiple polylogarithms preprint, January 2013

Leading singularities and off-shell conformal integrals text, January 2013

Bethe Ansaetze for GKP strings text, January 2013

Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data text, January 2013

Quantum mechanics of null polygonal Wilson loops text, January 2014

Quantum spectral curve for arbitrary state/operator in AdS$_5$/CFT$_4$ text, January 2014

Nonsinglet pentagons and NMHV amplitudes text, January 2014

Graphical functions in parametric space text, January 2015

Clustering and the Three-Point Function text, January 2016

Bootstrapping a Five-Loop Amplitude Using Steinmann Relations text, January 2016

Hexagonalization of Correlation Functions text, January 2016

Heptagons from the Steinmann Cluster Bootstrap text, January 2016

Strings in flat space and pp waves from ${\cal N}=4$ Super Yang Mills text, January 2002

Multi-loop Feynman integrals and conformal quantum mechanics text, January 2003

Continuum limit of fishnet graphs and AdS sigma model journal, January 2019

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

Twistor fishnets journal, January 2020

Octagons I: combinatorics and non-planar resummations other, January 2019

The double pentaladder integral to all ordersC text, January 2018

Numbers and Functions in Quantum Field Theory text, January 2016

Yangian Symmetry for Fishnet Feynman Graphs text, January 2017

The Double Pentaladder Integral to All Orders text, January 2018

Generalized Fishnets and Exact Four-Point Correlators in Chiral CFT$_4$ text, January 2019

Twistor fishnets text, January 2019

Polylogarithmes multiples uniformes en une variable
journal, April 2004

Publisher’s Note: New Integrable 4D Quantum Field Theories from Strongly Deformed Planar $N = 4$ Supersymmetric Yang-Mills Theory [Phys. Rev. Lett. 117 , 201602 (2016)]
journal, December 2016

Heptagons from the Steinmann cluster bootstrap
journal, February 2017

Space-time S-matrix and flux-tube S-matrix III. The two-particle contributions
journal, August 2014

Comments on operators with large spin
journal, November 2007

Space-time S-matrix and flux tube S-matrix II. Extracting and matching data
journal, January 2014

Asymptotic dispersion relation for the six-particle amplitude
journal, October 1982

N=4 supersymmetric Yang–Mills scattering amplitudes at high energies: the Regge cut contribution
journal, December 2009

Summation of an infinite series of ladder diagrams
journal, June 1993

Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations
journal, October 2016

Quantum mechanics of null polygonal Wilson loops
journal, May 2014

Quantum spectral curve for arbitrary state/operator in AdS5/CFT4
journal, September 2015

Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
journal, December 2016

Strings in flat space and pp waves from Script N = 4 Super Yang Mills
journal, April 2002

An operator product expansion for polygonal null Wilson loops
journal, April 2011

Hexagonalization of correlation functions
journal, January 2017

Optical theorems and steinmann relations
journal, April 1975

Review of AdS/CFT Integrability: An Overview
journal, October 2011

New Integrable 4D Quantum Field Theories from Strongly Deformed Planar $N = 4$ Supersymmetric Yang-Mills Theory
journal, November 2016

BFKL Pomeron, Reggeized gluons, and Bern-Dixon-Smirnov amplitudes
journal, August 2009

A semi-classical limit of the gauge/string correspondence
journal, August 2002

Exponential suppression with four legs and an infinity of loops
journal, August 2010

Separation of variables for the quantum SL( 2,Bbb R ) spin chain
journal, July 2003

Magic identities for conformal four-point integrals
journal, January 2007

“Fishing-net” diagrams as a completely integrable system
journal, November 1980

A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon
journal, March 2015

OPE for all helicity amplitudes II. Form factors and data analysis
journal, December 2015

Clustering and the three-point function
journal, October 2016

Multi-loop Feynman integrals and conformal quantum mechanics
journal, July 2003

Uniqueness of two-loop master contours
journal, October 2012

Quantum Spectral Curve for Planar $N = 4$ Super-Yang-Mills Theory
journal, January 2014

Bethe ansätze for GKP strings
journal, February 2014

Exact results for three- and four-point ladder diagrams with an arbitrary number of rungs
journal, May 1993

Graphical functions and single-valued multiple polylogarithms
journal, January 2014

Gluing hexagons at three loops
journal, June 2016

Nonsinglet pentagons and NMHV amplitudes
journal, July 2015

Bootstrapping the three-loop hexagon
journal, November 2011

Spacetime and Flux Tube $S$ -Matrices at Finite Coupling for $N = 4$ Supersymmetric Yang-Mills Theory
journal, August 2013

Graphical functions in parametric space
journal, December 2016

Leading singularities and off-shell conformal integrals
journal, August 2013

Generalised ladders and single-valued polylogs
journal, February 2013

Generalised Ladders and Single-valued Polylogs
text, January 2012

Heptagons from the Steinmann Cluster Bootstrap
text, January 2017

Leading singularities and off-shell conformal integrals
text, January 2013

Quantum mechanics of null polygonal Wilson loops
text, January 2014

Quantum mechanics of null polygonal Wilson loops
text, January 2014

BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
text, January 2008

N=4 supersymmetric Yang Mills scattering amplitudes at high energies: the Regge cut contribution
text, January 2008

An Operator Product Expansion for Polygonal null Wilson Loops
text, January 2010

Review of AdS/CFT Integrability: An Overview
text, January 2010

Bootstrapping the three-loop hexagon
text, January 2011

Uniqueness of two-loop master contours
text, January 2012

Graphical functions and single-valued multiple polylogarithms
preprint, January 2013

Leading singularities and off-shell conformal integrals
text, January 2013

Bethe Ansaetze for GKP strings
text, January 2013

Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data
text, January 2013

Quantum mechanics of null polygonal Wilson loops
text, January 2014

Quantum spectral curve for arbitrary state/operator in AdS$_5$/CFT$_4$
text, January 2014

Nonsinglet pentagons and NMHV amplitudes
text, January 2014

Graphical functions in parametric space
text, January 2015

Clustering and the Three-Point Function
text, January 2016

Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
text, January 2016

Hexagonalization of Correlation Functions
text, January 2016

Heptagons from the Steinmann Cluster Bootstrap
text, January 2016

Strings in flat space and pp waves from ${\cal N}=4$ Super Yang Mills
text, January 2002

Multi-loop Feynman integrals and conformal quantum mechanics
text, January 2003

Continuum limit of fishnet graphs and AdS sigma model
journal, January 2019

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

Twistor fishnets
journal, January 2020

Octagons I: combinatorics and non-planar resummations
other, January 2019

The double pentaladder integral to all ordersC
text, January 2018

Numbers and Functions in Quantum Field Theory
text, January 2016

Yangian Symmetry for Fishnet Feynman Graphs
text, January 2017

The Double Pentaladder Integral to All Orders
text, January 2018

Generalized Fishnets and Exact Four-Point Correlators in Chiral CFT$_4$
text, January 2019

Twistor fishnets
text, January 2019