On-shell structures of MHV amplitudes beyond the planar limit

Arkani-Hamed, Nima; Bourjaily, Jacob L.; Cachazo, Freddy; Postnikov, Alexander; Trnka, Jaroslav

doi:10.1007/JHEP06(2015)179

Title: On-shell structures of MHV amplitudes beyond the planar limit

Abstract

We initiate an exploration of on-shell functions in N=4 SYM beyond the planar limit by providing compact, combinatorial expressions for all leading singularities of MHV amplitudes and showing that they can always be expressed as a positive sum of differently ordered Parke-Taylor tree amplitudes. This is understood in terms of an extended notion of positivity in G(2, n), the Grassmannian of 2-planes in n dimensions: a single on-shell diagram can be associated with many different “positive” regions, of which the familiar G₊(2, n) associated with planar diagrams is just one example. The decomposition into Parke-Taylor factors is simply a “triangulation” of these extended positive regions. The U(1) decoupling and Kleiss-Kuijf (KK) relations satisfied by the Parke-Taylor amplitudes also follow naturally from this geometric picture. Finally, these results suggest that non-planar MHV amplitudes in N=4 SYM at all loop orders can be expressed as a sum of polylogarithms weighted by color factors and (unordered) Parke-Taylor amplitudes.

Authors:

Arkani-Hamed, Nima ^[1]; Bourjaily, Jacob L. ^[2]; Cachazo, Freddy ^[3]; Postnikov, Alexander ^[4]; Trnka, Jaroslav ^[5]

Inst. for Advanced Study, Princeton, NJ (United States)
Univ. of Copenhagen (Denmark). The Niels Bohr Inst.
Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
California Inst. of Technology (CalTech), Pasadena, CA (United States)

Publication Date:: Thu Jun 25 00:00:00 EDT 2015

Research Org.:: California Institute of Technology (CalTech), Pasadena, CA (United States)

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

OSTI Identifier:: 1441132

Grant/Contract Number:: SC0011632; FG02-91ER40654

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: 2015; Journal Issue: 6; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Scattering Amplitudes; 1/N Expansion; Supersymmetric gauge theory

Citation Formats


                    Arkani-Hamed, Nima, Bourjaily, Jacob L., Cachazo, Freddy, Postnikov, Alexander, and Trnka, Jaroslav. On-shell structures of MHV amplitudes beyond the planar limit.  United States: N. p., 2015. 
Web.  doi:10.1007/JHEP06(2015)179.

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                    Arkani-Hamed, Nima, Bourjaily, Jacob L., Cachazo, Freddy, Postnikov, Alexander, & Trnka, Jaroslav. On-shell structures of MHV amplitudes beyond the planar limit.  United States.  https://doi.org/10.1007/JHEP06(2015)179

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                    Arkani-Hamed, Nima, Bourjaily, Jacob L., Cachazo, Freddy, Postnikov, Alexander, and Trnka, Jaroslav. Thu .  
"On-shell structures of MHV amplitudes beyond the planar limit".  United States.  https://doi.org/10.1007/JHEP06(2015)179.  https://www.osti.gov/servlets/purl/1441132.

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@article{osti_1441132,

  title        = {On-shell structures of MHV amplitudes beyond the planar limit},

  author       = {Arkani-Hamed, Nima and Bourjaily, Jacob L. and Cachazo, Freddy and Postnikov, Alexander and Trnka, Jaroslav},

  abstractNote = {We initiate an exploration of on-shell functions in N=4 SYM beyond the planar limit by providing compact, combinatorial expressions for all leading singularities of MHV amplitudes and showing that they can always be expressed as a positive sum of differently ordered Parke-Taylor tree amplitudes. This is understood in terms of an extended notion of positivity in G(2, n), the Grassmannian of 2-planes in n dimensions: a single on-shell diagram can be associated with many different “positive” regions, of which the familiar G+(2, n) associated with planar diagrams is just one example. The decomposition into Parke-Taylor factors is simply a “triangulation” of these extended positive regions. The U(1) decoupling and Kleiss-Kuijf (KK) relations satisfied by the Parke-Taylor amplitudes also follow naturally from this geometric picture. Finally, these results suggest that non-planar MHV amplitudes in N=4 SYM at all loop orders can be expressed as a sum of polylogarithms weighted by color factors and (unordered) Parke-Taylor amplitudes.},

  doi          = {10.1007/JHEP06(2015)179},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 6,

  volume       = 2015,

  place        = {United States},

  year         = {Thu Jun 25 00:00:00 EDT 2015},

  month        = {Thu Jun 25 00:00:00 EDT 2015}

}

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Works referenced in this record:

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Works referencing / citing this record:

On-shell diagrams, Graßmannians and integrability for form factors
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Frassek, Rouven; Meidinger, David; Nandan, Dhritiman
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Herrmann, Enrico; Trnka, Jaroslav
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Title: On-shell structures of MHV amplitudes beyond the planar limit

Abstract

Citation Formats

Singularity Structure of Maximally Supersymmetric Scattering Amplitudes journal, December 2014

Multigluon cross sections and 5-jet production at hadron colliders journal, January 1989

Perturbative Quantum Gravity as a Double Copy of Gauge Theory journal, August 2010

Amplitude for n -Gluon Scattering journal, June 1986

Total Positivity in Reductive Groups book, January 1994

The Structure of Multiloop Amplitudes in Gauge and Gravity Theories journal, August 2010

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

A duality for the S matrix journal, March 2010

Canonical bases arising from quantized enveloping algebras journal, May 1990

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A complete two-loop, five-gluon helicity amplitude in Yang-Mills theory journal, October 2015

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A Complete Two-Loop, Five-Gluon Helicity Amplitude in Yang-Mills Theory text, January 2015

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Cluster Algebras and the Subalgebra Constructibility of the Seven-Particle Remainder Function text, January 2018

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Analytic result for a two-loop five-particle amplitude text, January 2018

The two-loop five-point amplitude in $\mathcal N=8$ supergravity text, January 2019

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Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
journal, December 2014

Multigluon cross sections and 5-jet production at hadron colliders
journal, January 1989

Perturbative Quantum Gravity as a Double Copy of Gauge Theory
journal, August 2010

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

Total Positivity in Reductive Groups
book, January 1994

The Structure of Multiloop Amplitudes in Gauge and Gravity Theories
journal, August 2010

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

A duality for the S matrix
journal, March 2010

Canonical bases arising from quantized enveloping algebras
journal, May 1990

Positroid varieties: juggling and geometry
journal, August 2013

On-shell diagrams, Graßmannians and integrability for form factors
journal, January 2016

Δ-algebra and scattering amplitudes
journal, February 2019

A complete two-loop, five-gluon helicity amplitude in Yang-Mills theory
journal, October 2015

Bipartite field theories and D-brane instantons
journal, November 2018

Positivity, Grassmannian geometry and simplex-like structures of scattering amplitudes
journal, December 2017

Top-forms of leading singularities in nonplanar multi-loop amplitudes
journal, February 2018

Analytic Result for a Two-Loop Five-Particle Amplitude
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A Complete Two-Loop, Five-Gluon Helicity Amplitude in Yang-Mills Theory
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Evidence for a Nonplanar Amplituhedron
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Full Colour for Loop Amplitudes in Yang-Mills Theory
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Prescriptive Unitarity
text, January 2017

Bipartite field theories and D-brane instantons
text, January 2018

Cluster Algebras and the Subalgebra Constructibility of the Seven-Particle Remainder Function
text, January 2018

Two-loop $\mathcal{N}=2$ SQCD amplitudes with external matter from iterated cuts
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