Dual Conformal Structure Beyond the Planar Limit

Bern, Zvi; Enciso, Michael; Shen, Chia-Hsien; Zeng, Mao

doi:10.1103/PhysRevLett.121.121603

Title: Dual Conformal Structure Beyond the Planar Limit

Abstract

The planar scattering amplitudes of N = 4 super-Yang-Mills theory display symmetries and structures which underlie their relatively simple analytic properties such as having only logarithmic singularities and no poles at infinity. Recent work shows in various nontrivial examples that the simple analytic properties of the planar sector survive into the nonplanar sector, but this has yet to be understood from underlying symmetries. Here, we explicitly show that for an infinite class of nonplanar integrals that covers all subleading-color contributions to the two-loop four- and five-point amplitudes of N = 4 super-Yang-Mills theory, symmetries analogous to dual conformal invariance exist. A natural conjecture is that this continues to all amplitudes of the theory at any loop order.

Authors:: Bern, Zvi; Enciso, Michael; Shen, Chia-Hsien; Zeng, Mao

Publication Date:: Sat Sep 01 00:00:00 EDT 2018

Research Org.:: Univ. of California, Los Angeles, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1471787

Alternate Identifier(s):: OSTI ID: 1498982

Grant/Contract Number:: SC0009937

Resource Type:: Published Article

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Name: Physical Review Letters Journal Volume: 121 Journal Issue: 12; 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


                    Bern, Zvi, Enciso, Michael, Shen, Chia-Hsien, and Zeng, Mao. Dual Conformal Structure Beyond the Planar Limit.  United States: N. p., 2018. 
Web.  doi:10.1103/PhysRevLett.121.121603.

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                    Bern, Zvi, Enciso, Michael, Shen, Chia-Hsien, & Zeng, Mao. Dual Conformal Structure Beyond the Planar Limit.  United States.  https://doi.org/10.1103/PhysRevLett.121.121603

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                    Bern, Zvi, Enciso, Michael, Shen, Chia-Hsien, and Zeng, Mao. Sat .  
"Dual Conformal Structure Beyond the Planar Limit".  United States.  https://doi.org/10.1103/PhysRevLett.121.121603.

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@article{osti_1471787,

  title        = {Dual Conformal Structure Beyond the Planar Limit},

  author       = {Bern, Zvi and Enciso, Michael and Shen, Chia-Hsien and Zeng, Mao},

  abstractNote = {The planar scattering amplitudes of N = 4 super-Yang-Mills theory display symmetries and structures which underlie their relatively simple analytic properties such as having only logarithmic singularities and no poles at infinity. Recent work shows in various nontrivial examples that the simple analytic properties of the planar sector survive into the nonplanar sector, but this has yet to be understood from underlying symmetries. Here, we explicitly show that for an infinite class of nonplanar integrals that covers all subleading-color contributions to the two-loop four- and five-point amplitudes of N = 4 super-Yang-Mills theory, symmetries analogous to dual conformal invariance exist. A natural conjecture is that this continues to all amplitudes of the theory at any loop order.},

  doi          = {10.1103/PhysRevLett.121.121603},

  journal      = {Physical Review Letters},

  number       = 12,

  volume       = 121,

  place        = {United States},

  year         = {Sat Sep 01 00:00:00 EDT 2018},

  month        = {Sat Sep 01 00:00:00 EDT 2018}

}

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Cited by: 21 works

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Figure 1: Planar double box with dual coordinates and the crossed-box related to it by moving leg 3 to the central rung.

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Works referenced in this record:

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Yangian-type symmetries of non-planar leading singularities
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Yangian symmetry of scattering amplitudes in 𝒩 = 4 super Yang-Mills theory
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Figures / Tables found in this record:

Figure 1 (p. 2)

Figure 2 (p. 3)

Figure 3 (p. 4)

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Title: Dual Conformal Structure Beyond the Planar Limit

Abstract

Citation Formats

Figures / Tables:

Singularity Structure of Maximally Supersymmetric Scattering Amplitudes journal, December 2014

Heptagons from the Steinmann cluster bootstrap journal, February 2017

Analytic Form of the Two-Loop Planar Five-Gluon All-Plus-Helicity Amplitude in QCD journal, February 2016

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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

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

The SYM integrable super spin chain journal, October 2003

Multiloop Integrals in Dimensional Regularization Made Simple journal, June 2013

Three-loop universal anomalous dimension of the Wilson operators in N=4 SUSY Yang–Mills model journal, August 2004

The Amplituhedron journal, October 2014

Differential equations for loop integrals in Baikov representation journal, May 2018

Duality and multi-gluon scattering journal, March 1988

Evidence for a nonplanar amplituhedron journal, June 2016

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

Gluon scattering amplitudes at strong coupling journal, June 2007

Connection between Feynman integrals having different values of the space-time dimension journal, November 1996

The Sudakov form factor at four loops in maximal super Yang-Mills theory journal, January 2018

Into the amplituhedron journal, December 2014

Colour-dressed hexagon tessellations for correlation functions and non-planar corrections journal, February 2018

Four-loop planar amplitude and cusp anomalous dimension in maximally supersymmetric Yang-Mills theory journal, April 2007

On-shell structures of MHV amplitudes beyond the planar limit journal, June 2015

Differential equations on unitarity cut surfaces journal, June 2017

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

Dual superconformal symmetry of scattering amplitudes in super-Yang–Mills theory journal, March 2010

The complete planar S-matrix of $ \mathcal{N} = 4 $ SYM as a Wilson loop in twistor space journal, December 2010

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

Yangian-type symmetries of non-planar leading singularities journal, May 2016

Yangian symmetry of scattering amplitudes in 𝒩 = 4 super Yang-Mills theory journal, May 2009

Logarithmic singularities and maximally supersymmetric amplitudes journal, June 2015

Bootstrapping pentagon functions journal, May 2018

The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM journal, January 2011

Scattering Amplitudes from Superconformal Ward Identities journal, July 2018

Stratifying on-shell cluster varieties: the geometry of non-planar on-shell diagrams journal, October 2016

Dimensionally regulated one-loop integrals journal, March 1993

Amplitude for n -Gluon Scattering journal, June 1986

Classical Polylogarithms for Amplitudes and Wilson Loops journal, October 2010

Dual conformal symmetry, integration-by-parts reduction, differential equations, and the nonplanar sector journal, November 2017

Non-planar on-shell diagrams journal, June 2015

Hidden symmetries of the AdS 5 × S 5 superstring journal, February 2004

Erratum to: “Three-loop universal anomalous dimension of the Wilson operators in N = 4 SUSY Yang–Mills model” [Phys. Lett. B 595 (2004) 521] journal, January 2006

Five-point amplitudes in N = 4 super-Yang-Mills theory and N = 8 supergravity journal, January 2012

On Yangian-invariant regularization of deformed on-shell diagrams in $\mathcal{N}=4$ super-Yang–Mills theory journal, August 2014

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

On the highest transcendentality in SUSY journal, May 2007

Dimensionally-regulated pentagon integrals journal, January 1994

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

Erratum: Analytic Form of the Two-Loop Planar Five-Gluon All-Plus-Helicity Amplitude in QCD [Phys. Rev. Lett. 116 , 062001 (2016)] journal, May 2016

Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
journal, December 2014

Heptagons from the Steinmann cluster bootstrap
journal, February 2017

Analytic Form of the Two-Loop Planar Five-Gluon All-Plus-Helicity Amplitude in QCD
journal, February 2016

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

Are scattering amplitudes dual to super Wilson loops?
journal, February 2012

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

The SYM integrable super spin chain
journal, October 2003

Multiloop Integrals in Dimensional Regularization Made Simple
journal, June 2013

Three-loop universal anomalous dimension of the Wilson operators in N=4 SUSY Yang–Mills model
journal, August 2004

The Amplituhedron
journal, October 2014

Differential equations for loop integrals in Baikov representation
journal, May 2018

Duality and multi-gluon scattering
journal, March 1988

Evidence for a nonplanar amplituhedron
journal, June 2016

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

Gluon scattering amplitudes at strong coupling
journal, June 2007

Connection between Feynman integrals having different values of the space-time dimension
journal, November 1996

The Sudakov form factor at four loops in maximal super Yang-Mills theory
journal, January 2018

Into the amplituhedron
journal, December 2014

Colour-dressed hexagon tessellations for correlation functions and non-planar corrections
journal, February 2018

Four-loop planar amplitude and cusp anomalous dimension in maximally supersymmetric Yang-Mills theory
journal, April 2007

On-shell structures of MHV amplitudes beyond the planar limit
journal, June 2015

Differential equations on unitarity cut surfaces
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Spacetime and Flux Tube $S$ -Matrices at Finite Coupling for $N = 4$ Supersymmetric Yang-Mills Theory
journal, August 2013

Dual superconformal symmetry of scattering amplitudes in super-Yang–Mills theory
journal, March 2010

The complete planar S-matrix of $ \mathcal{N} = 4 $ SYM as a Wilson loop in twistor space
journal, December 2010

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

Yangian-type symmetries of non-planar leading singularities
journal, May 2016

Yangian symmetry of scattering amplitudes in 𝒩 = 4 super Yang-Mills theory
journal, May 2009

Logarithmic singularities and maximally supersymmetric amplitudes
journal, June 2015

Bootstrapping pentagon functions
journal, May 2018

The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM
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journal, July 2018

Stratifying on-shell cluster varieties: the geometry of non-planar on-shell diagrams
journal, October 2016

Dimensionally regulated one-loop integrals
journal, March 1993

Amplitude for $n$ -Gluon Scattering
journal, June 1986

Classical Polylogarithms for Amplitudes and Wilson Loops
journal, October 2010

Dual conformal symmetry, integration-by-parts reduction, differential equations, and the nonplanar sector
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Non-planar on-shell diagrams
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Hidden symmetries of the ${AdS}_{5} \times S^{5}$ superstring
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Erratum to: “Three-loop universal anomalous dimension of the Wilson operators in $N = 4$ SUSY Yang–Mills model” [Phys. Lett. B 595 (2004) 521]
journal, January 2006

Five-point amplitudes in $N = 4$ super-Yang-Mills theory and $N = 8$ supergravity
journal, January 2012

On Yangian-invariant regularization of deformed on-shell diagrams in $\mathcal{N}=4$ super-Yang–Mills theory
journal, August 2014

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

On the highest transcendentality in SUSY
journal, May 2007

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

Erratum: Analytic Form of the Two-Loop Planar Five-Gluon All-Plus-Helicity Amplitude in QCD [Phys. Rev. Lett. 116 , 062001 (2016)]
journal, May 2016