Origin of the Six-Gluon Amplitude in Planar N = 4 Supersymmetric Yang-Mills Theory

Basso, Benjamin; Dixon, Lance J.; Papathanasiou, Georgios

doi:10.1103/PhysRevLett.124.161603

Title: Origin of the Six-Gluon Amplitude in Planar $N = 4$ Supersymmetric Yang-Mills Theory

Abstract

We study the maximally-helicity-violating six-gluon scattering amplitude in planar $N = 4$ super-Yang-Mills theory at finite coupling when all three cross ratios are small. It exhibits a double logarithmic scaling in the cross ratios, controlled by a handful of “anomalous dimensions” that are functions of the coupling constant alone. Inspired by known seven-loop results at weak coupling and the integrability-based pentagon operator product expansion, we present conjectures for the all-order resummation of these anomalous dimensions. At strong coupling, our predictions agree perfectly with the string theory analysis. Intriguingly, the simplest of these anomalous dimensions coincides with one describing the lightlike limit of the octagon, namely, the four-point function of large-charge Bogomol’nyi–Prasad–Sommerfield (BPS) operators.

Authors:

Basso, Benjamin;

;

Publication Date:: Wed Apr 22 00:00:00 EDT 2020

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

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP); French National Agency for Research

OSTI Identifier:: 1615708

Alternate Identifier(s):: OSTI ID: 1616294

Report Number(s):: SLAC-PUB-17501
Journal ID: ISSN 0031-9007; PRLTAO; 161603

Grant/Contract Number:: AC02-76SF00515; ANR-17-CE31-0001-02

Resource Type:: Published Article

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Name: Physical Review Letters Journal Volume: 124 Journal Issue: 16; Journal ID: ISSN 0031-9007

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; field & string theory models & techniques; quantum field theory; scattering amplitudes

Citation Formats


                    Basso, Benjamin, Dixon, Lance J., and Papathanasiou, Georgios. Origin of the Six-Gluon Amplitude in Planar N = 4 Supersymmetric Yang-Mills Theory.  United States: N. p., 2020. 
Web.  doi:10.1103/PhysRevLett.124.161603.

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                    Basso, Benjamin, Dixon, Lance J., & Papathanasiou, Georgios. Origin of the Six-Gluon Amplitude in Planar N = 4 Supersymmetric Yang-Mills Theory.  United States.  https://doi.org/10.1103/PhysRevLett.124.161603

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                    Basso, Benjamin, Dixon, Lance J., and Papathanasiou, Georgios. Wed .  
"Origin of the Six-Gluon Amplitude in Planar N = 4 Supersymmetric Yang-Mills Theory".  United States.  https://doi.org/10.1103/PhysRevLett.124.161603.

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@article{osti_1615708,

  title        = {Origin of the Six-Gluon Amplitude in Planar N = 4 Supersymmetric Yang-Mills Theory},

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

  abstractNote = {We study the maximally-helicity-violating six-gluon scattering amplitude in planar N=4 super-Yang-Mills theory at finite coupling when all three cross ratios are small. It exhibits a double logarithmic scaling in the cross ratios, controlled by a handful of “anomalous dimensions” that are functions of the coupling constant alone. Inspired by known seven-loop results at weak coupling and the integrability-based pentagon operator product expansion, we present conjectures for the all-order resummation of these anomalous dimensions. At strong coupling, our predictions agree perfectly with the string theory analysis. Intriguingly, the simplest of these anomalous dimensions coincides with one describing the lightlike limit of the octagon, namely, the four-point function of large-charge Bogomol’nyi–Prasad–Sommerfield (BPS) operators.},

  doi          = {10.1103/PhysRevLett.124.161603},

  journal      = {Physical Review Letters},

  number       = 16,

  volume       = 124,

  place        = {United States},

  year         = {Wed Apr 22 00:00:00 EDT 2020},

  month        = {Wed Apr 22 00:00:00 EDT 2020}

}

Copy to clipboard

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Works referenced in this record:

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Dixon, Lance J.; Drummond, James; Harrington, Thomas
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MHV amplitudes at strong coupling and linearized TBA equations
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Hexagonalization of correlation functions
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Journal of High Energy Physics, Vol. 2017, Issue 1
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Fermionic pentagons and NMHV hexagon
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Two-loop six-gluon maximally helicity violating amplitude in maximally supersymmetric Yang-Mills theory
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The octagon as a determinant
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Thermodynamic bubble ansatz
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Gluon scattering amplitudes at strong coupling
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Alday, Luis F.; Maldacena, Juan
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Test of the Anti–de Sitter-Space/Conformal-Field-Theory Correspondence Using High-Spin Operators
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Space-time S-matrix and flux-tube S-matrix IV. Gluons and fusion
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Basso, Benjamin; Sever, Amit; Vieira, Pedro
Journal of High Energy Physics, Vol. 2014, Issue 9
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A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon
journal, March 2015

Drummond, J. M.; Papathanasiou, G.; Spradlin, M.
Journal of High Energy Physics, Vol. 2015, Issue 3
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Cluster adjacency and the four-loop NMHV heptagon
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Hexagon OPE resummation and multi-Regge kinematics
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Perturbative four-point functions in planar N = 4 $$ \mathcal{N}=4 $$ SYM From hexagonalization
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The four-loop six-gluon NMHV ratio function
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Graphical functions and single-valued multiple polylogarithms
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Schnetz, Oliver
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Hexagon Wilson loop = six-gluon MHV amplitude
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Bootstrapping the three-loop hexagon
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Nonsinglet pentagons and NMHV amplitudes
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Spacetime and Flux Tube $S$ -Matrices at Finite Coupling for $N = 4$ Supersymmetric Yang-Mills Theory
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Basso, Benjamin; Sever, Amit; Vieira, Pedro
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Hexagon Wilson loop OPE and harmonic polylogarithms
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Papathanasiou, Georgios
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Works referencing / citing this record:

The Origin of the Six-Gluon Amplitude in Planar $\mathcal{N}=4$ SYM
text, January 2020

Basso, Benjamin; Dixon, Lance J.; Papathanasiou, Georgios
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2020-01802

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Title: Origin of the Six-Gluon Amplitude in Planar N = 4 Supersymmetric Yang-Mills Theory

Abstract

Citation Formats

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

From correlation functions to Wilson loops journal, September 2011

Lüscher formula for GKP string journal, July 2012

Collinear Limit of Scattering Amplitudes at Strong Coupling journal, December 2014

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

Conformal properties of four-gluon planar amplitudes and Wilson loops journal, May 2008

Bootstrapping an NMHV amplitude through three loops journal, October 2014

Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond journal, October 2005

The Galois coaction on $\phi^4$ periods journal, January 2017

Hexagon functions and the three-loop remainder function journal, December 2013

On planar gluon amplitudes/Wilson loops duality journal, May 2008

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

Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes journal, February 2010

Feynman amplitudes, coaction principle, and cosmic Galois group journal, January 2017

MHV amplitudes in super-Yang–Mills and Wilson Loops journal, May 2008

Six-Gluon amplitudes in planar N$$ \mathcal{N} $$ = 4 super-Yang-Mills theory at six and seven loops journal, August 2019

The cosmic Galois group and extended Steinmann relations for planar N$$ \mathcal{N} $$ = 4 SYM amplitudes journal, September 2019

MHV amplitudes at strong coupling and linearized TBA equations journal, August 2018

Tessellating cushions: four-point functions in N $$ \mathcal{N} $$ = 4 SYM journal, October 2017

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

Hexagonalization of correlation functions journal, January 2017

Fermionic pentagons and NMHV hexagon journal, May 2015

Two-loop six-gluon maximally helicity violating amplitude in maximally supersymmetric Yang-Mills theory journal, August 2008

The octagon as a determinant journal, November 2019

Thermodynamic bubble ansatz journal, September 2011

Gluon scattering amplitudes at strong coupling journal, June 2007

Test of the Anti–de Sitter-Space/Conformal-Field-Theory Correspondence Using High-Spin Operators journal, March 2007

Space-time S-matrix and flux-tube S-matrix IV. Gluons and fusion journal, September 2014

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

Cluster adjacency and the four-loop NMHV heptagon journal, March 2019

Hexagon OPE resummation and multi-Regge kinematics journal, February 2016

Classical Polylogarithms for Amplitudes and Wilson Loops journal, October 2010

Determinant Formula for the Octagon Form Factor in N = 4 Supersymmetric Yang-Mills Theory journal, June 2019

Pulling the straps of polygons journal, December 2011

Perturbative four-point functions in planar N = 4 $$ \mathcal{N}=4 $$ SYM From hexagonalization journal, January 2019

Hexagonal Wilson loops in planar ${ \mathcal N }=4$ SYM theory at finite coupling journal, September 2016

Evaluating the six-point remainder function near the collinear limit journal, October 2014

The four-loop six-gluon NMHV ratio function journal, January 2016

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

Hexagon Wilson loop = six-gluon MHV amplitude journal, July 2009

Bootstrapping the three-loop hexagon journal, November 2011

Nonsinglet pentagons and NMHV amplitudes journal, July 2015

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

On the strong coupling scaling dimension of high spin operators journal, April 2007

Transcendentality and crossing journal, January 2007

The four-loop remainder function and multi-Regge behavior at NNLLA in planar $ \mathcal{N} $ = 4 super-Yang-Mills theory journal, June 2014

Hexagon Wilson loop OPE and harmonic polylogarithms journal, November 2013

The Origin of the Six-Gluon Amplitude in Planar $\mathcal{N}=4$ SYM text, January 2020

Title: Origin of the Six-Gluon Amplitude in Planar $N = 4$ Supersymmetric Yang-Mills Theory

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

From correlation functions to Wilson loops
journal, September 2011

Lüscher formula for GKP string
journal, July 2012

Collinear Limit of Scattering Amplitudes at Strong Coupling
journal, December 2014

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

Conformal properties of four-gluon planar amplitudes and Wilson loops
journal, May 2008

Bootstrapping an NMHV amplitude through three loops
journal, October 2014

Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond
journal, October 2005

The Galois coaction on $\phi^4$ periods
journal, January 2017

Hexagon functions and the three-loop remainder function
journal, December 2013

On planar gluon amplitudes/Wilson loops duality
journal, May 2008

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

Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
journal, February 2010

Feynman amplitudes, coaction principle, and cosmic Galois group
journal, January 2017

MHV amplitudes in super-Yang–Mills and Wilson Loops
journal, May 2008

Six-Gluon amplitudes in planar N$$ \mathcal{N} $$ = 4 super-Yang-Mills theory at six and seven loops
journal, August 2019

The cosmic Galois group and extended Steinmann relations for planar N$$ \mathcal{N} $$ = 4 SYM amplitudes
journal, September 2019

MHV amplitudes at strong coupling and linearized TBA equations
journal, August 2018

Tessellating cushions: four-point functions in N $$ \mathcal{N} $$ = 4 SYM
journal, October 2017

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

Hexagonalization of correlation functions
journal, January 2017

Fermionic pentagons and NMHV hexagon
journal, May 2015

Two-loop six-gluon maximally helicity violating amplitude in maximally supersymmetric Yang-Mills theory
journal, August 2008

The octagon as a determinant
journal, November 2019

Thermodynamic bubble ansatz
journal, September 2011

Gluon scattering amplitudes at strong coupling
journal, June 2007

Test of the Anti–de Sitter-Space/Conformal-Field-Theory Correspondence Using High-Spin Operators
journal, March 2007

Space-time S-matrix and flux-tube S-matrix IV. Gluons and fusion
journal, September 2014

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

Cluster adjacency and the four-loop NMHV heptagon
journal, March 2019

Hexagon OPE resummation and multi-Regge kinematics
journal, February 2016

Classical Polylogarithms for Amplitudes and Wilson Loops
journal, October 2010

Determinant Formula for the Octagon Form Factor in $N = 4$ Supersymmetric Yang-Mills Theory
journal, June 2019

Pulling the straps of polygons
journal, December 2011

Perturbative four-point functions in planar N = 4 $$ \mathcal{N}=4 $$ SYM From hexagonalization
journal, January 2019

Hexagonal Wilson loops in planar ${ \mathcal N }=4$ SYM theory at finite coupling
journal, September 2016

Evaluating the six-point remainder function near the collinear limit
journal, October 2014

The four-loop six-gluon NMHV ratio function
journal, January 2016

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

Hexagon Wilson loop = six-gluon MHV amplitude
journal, July 2009

Bootstrapping the three-loop hexagon
journal, November 2011

Nonsinglet pentagons and NMHV amplitudes
journal, July 2015

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

On the strong coupling scaling dimension of high spin operators
journal, April 2007

Transcendentality and crossing
journal, January 2007

The four-loop remainder function and multi-Regge behavior at NNLLA in planar $ \mathcal{N} $ = 4 super-Yang-Mills theory
journal, June 2014

Hexagon Wilson loop OPE and harmonic polylogarithms
journal, November 2013

The Origin of the Six-Gluon Amplitude in Planar $\mathcal{N}=4$ SYM
text, January 2020