All-loop cuts from the Amplituhedron

Langer, Cameron; Srikant, Akshay Yelleshpur

doi:10.1007/jhep04(2019)105

Title: All-loop cuts from the Amplituhedron

Abstract

The definition of the amplituhedron in terms of sign flips involves both one-loop constraints and the “mutual positivity” constraint. To gain an understanding of the all-loop integrand of $ \mathcal{N}=4 $ sYM requires understanding the crucial role played by mutual positivity. This paper is an attempt towards developing a procedure to introduce the complexities of mutual positivity in a systematic and controlled manner. As the first step in this procedure, we trivialize these constraints and understand the geometry underlying the remaining constraints to all loops and multiplicities. We present a host of configurations which correspond to various faces of the amplituhedron. The results we derive are valid at all multiplicities and loop orders for the maximally helicity violating (MHV) configurations. These include detailed derivations for the results in. We conclude by indicating how one might move beyond trivial mutual positivity by presenting a series of configuration which re-introduce it bit by bit.

Authors:

^[1];

^[2]

Univ. of California, Davis, CA (United States)
Princeton Univ., NJ (United States)

Publication Date:: Mon Apr 15 00:00:00 EDT 2019

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

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

OSTI Identifier:: 1611304

Grant/Contract Number:: SC0009999

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: 2019; Journal Issue: 4; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics; Scattering Amplitudes; Supersymmetric Gauge Theory

Citation Formats


                    Langer, Cameron, and Srikant, Akshay Yelleshpur. All-loop cuts from the Amplituhedron.  United States: N. p., 2019. 
Web.  doi:10.1007/jhep04(2019)105.

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                    Langer, Cameron, & Srikant, Akshay Yelleshpur. All-loop cuts from the Amplituhedron.  United States.  https://doi.org/10.1007/jhep04(2019)105

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                    Langer, Cameron, and Srikant, Akshay Yelleshpur. Mon .  
"All-loop cuts from the Amplituhedron".  United States.  https://doi.org/10.1007/jhep04(2019)105.  https://www.osti.gov/servlets/purl/1611304.

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@article{osti_1611304,

  title        = {All-loop cuts from the Amplituhedron},

  author       = {Langer, Cameron and Srikant, Akshay Yelleshpur},

  abstractNote = {The definition of the amplituhedron in terms of sign flips involves both one-loop constraints and the “mutual positivity” constraint. To gain an understanding of the all-loop integrand of \( \mathcal{N}=4 \) sYM requires understanding the crucial role played by mutual positivity. This paper is an attempt towards developing a procedure to introduce the complexities of mutual positivity in a systematic and controlled manner. As the first step in this procedure, we trivialize these constraints and understand the geometry underlying the remaining constraints to all loops and multiplicities. We present a host of configurations which correspond to various faces of the amplituhedron. The results we derive are valid at all multiplicities and loop orders for the maximally helicity violating (MHV) configurations. These include detailed derivations for the results in. We conclude by indicating how one might move beyond trivial mutual positivity by presenting a series of configuration which re-introduce it bit by bit.},

  doi          = {10.1007/jhep04(2019)105},

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

  number       = 4,

  volume       = 2019,

  place        = {United States},

  year         = {Mon Apr 15 00:00:00 EDT 2019},

  month        = {Mon Apr 15 00:00:00 EDT 2019}

}

Copy to clipboard

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Works referenced in this record:

Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
journal, December 2014

Arkani-Hamed, Nima; Bourjaily, Jacob L.; Cachazo, Freddy
Physical Review Letters, Vol. 113, Issue 26
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The amplituhedron and the one-loop Grassmannian measure
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Logarithmic singularities and maximally supersymmetric amplitudes
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Bern, Zvi; Herrmann, Enrico; Litsey, Sean
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The Amplituhedron
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Arkani-Hamed, Nima; Trnka, Jaroslav
Journal of High Energy Physics, Vol. 2014, Issue 10
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Amplitudes and correlators to ten loops using simple, graphical bootstraps
journal, November 2016

Bourjaily, Jacob L.; Heslop, Paul; Tran, Vuong-Viet
Journal of High Energy Physics, Vol. 2016, Issue 11
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A note on polytopes for scattering amplitudes
journal, April 2012

Arkani-Hamed, N.; Bourjaily, J.; Cachazo, F.
Journal of High Energy Physics, Vol. 2012, Issue 4
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Ferro, Livia; Łukowski, Tomasz; Parisi, Matteo
Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 4
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Evidence for a nonplanar amplituhedron
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Logarithms and volumes of polytopes
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Notes on scattering amplitudes as differential forms
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Into the amplituhedron
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Arkani-Hamed, Nima; Trnka, Jaroslav
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All-loop Mondrian diagrammatics and 4-particle amplituhedron
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An, Yang; Li, Yi; Li, Zhinan
Journal of High Energy Physics, Vol. 2018, Issue 6
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Positive amplitudes in the amplituhedron
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Arkani-Hamed, Nima; Hodges, Andrew; Trnka, Jaroslav
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Unwinding the amplituhedron in binary
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Arkani-Hamed, Nima; Thomas, Hugh; Trnka, Jaroslav
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Scattering forms and the positive geometry of kinematics, color and the worldsheet
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Arkani-Hamed, Nima; Bai, Yuntao; He, Song
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Yangian symmetry for the tree amplituhedron
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Ferro, Livia; Łukowski, Tomasz; Orta, Andrea
Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 29
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Positive geometries and canonical forms
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Arkani-Hamed, Nima; Bai, Yuntao; Lam, Thomas
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The amplituhedron from momentum twistor diagrams
journal, February 2015

Bai, Yuntao; He, Song
Journal of High Energy Physics, Vol. 2015, Issue 2
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Eliminating spurious poles from gauge-theoretic amplitudes
journal, May 2013

Hodges, Andrew
Journal of High Energy Physics, Vol. 2013, Issue 5
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Deep Into the Amplituhedron: Amplitude Singularities at All Loops and Legs
journal, February 2019

Arkani-Hamed, Nima; Langer, Cameron; Srikant, Akshay Yelleshpur
Physical Review Letters, Vol. 122, Issue 5
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Local integrals for planar scattering amplitudes
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Arkani-Hamed, N.; Bourjaily, J.; Cachazo, F.
Journal of High Energy Physics, Vol. 2012, Issue 6
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4-particle amplituhedron at 3-loop and its Mondrian diagrammatic implication
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Rao, Junjie
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The soft-collinear bootstrap: $ \mathcal{N} = {4} $ Yang-Mills amplitudes at six- and seven-loops
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Bourjaily, J. L.; DiRe, A.; Shaikh, A.
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Perturbation Theory at Eight Loops: Novel Structures and the Breakdown of Manifest Conformality in $N = 4$ Supersymmetric Yang-Mills Theory
journal, May 2016

Bourjaily, Jacob L.; Heslop, Paul; Tran, Vuong-Viet
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Eliminating spurious poles from gauge-theoretic amplitudes
preprint, January 2009

Hodges, Andrew
arXiv
DOI: 10.48550/arxiv.0905.1473

Anatomy of the Amplituhedron
preprint, January 2014

Franco, Sebastian; Galloni, Daniele; Mariotti, Alberto
arXiv
DOI: 10.48550/arxiv.1408.3410

Positive Amplitudes In The Amplituhedron
text, January 2014

Arkani-Hamed, Nima; Hodges, Andrew; Trnka, Jaroslav
arXiv
DOI: 10.48550/arxiv.1412.8478

Logarithmic Singularities and Maximally Supersymmetric Amplitudes
preprint, January 2014

Bern, Zvi; Herrmann, Enrico; Litsey, Sean
arXiv
DOI: 10.48550/arxiv.1412.8584

Evidence for a Nonplanar Amplituhedron
text, January 2015

Bern, Zvi; Herrmann, Enrico; Litsey, Sean
arXiv
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Logarithms and Volumes of Polytopes
preprint, January 2016

Enciso, Michael
arXiv
DOI: 10.48550/arxiv.1612.07370

Unwinding the Amplituhedron in Binary
text, January 2017

Arkani-Hamed, Nima; Thomas, Hugh; Trnka, Jaroslav
arXiv
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All-loop Mondrian Diagrammatics and 4-particle Amplituhedron
text, January 2017

An, Yang; Li, Yi; Li, Zhinan
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Works referencing / citing this record:

Positive geometry, local triangulations, and the dual of the Amplituhedron
journal, January 2021

Herrmann, Enrico; Langer, Cameron; Trnka, Jaroslav
Journal of High Energy Physics, Vol. 2021, Issue 1
DOI: 10.1007/jhep01(2021)035

A Soft Theorem for the Tropical Grassmannian
preprint, January 2019

Sepúlveda, Diego García; Guevara, Alfredo
arXiv
DOI: 10.48550/arxiv.1909.05291

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Title: All-loop cuts from the Amplituhedron

Abstract

Citation Formats

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Dual Conformal Structure Beyond the Planar Limit journal, September 2018

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Eliminating spurious poles from gauge-theoretic amplitudes journal, May 2013

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Anatomy of the Amplituhedron preprint, January 2014

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Evidence for a Nonplanar Amplituhedron text, January 2015

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All-loop Mondrian Diagrammatics and 4-particle Amplituhedron text, January 2017

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Logarithmic singularities and maximally supersymmetric amplitudes
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A note on polytopes for scattering amplitudes
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Amplituhedron meets Jeffrey–Kirwan residue
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Evidence for a nonplanar amplituhedron
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Logarithms and volumes of polytopes
journal, April 2018

Notes on scattering amplitudes as differential forms
journal, October 2018

Into the amplituhedron
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All-loop Mondrian diagrammatics and 4-particle amplituhedron
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Positive amplitudes in the amplituhedron
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Volumes of polytopes without triangulations
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Scattering forms and the positive geometry of kinematics, color and the worldsheet
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Yangian symmetry for the tree amplituhedron
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Positive geometries and canonical forms
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The amplituhedron from momentum twistor diagrams
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Eliminating spurious poles from gauge-theoretic amplitudes
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Local integrals for planar scattering amplitudes
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