Unwinding the amplituhedron in binary

Arkani-Hamed, Nima; Thomas, Hugh; Trnka, Jaroslav

doi:10.1007/jhep01(2018)016

Title: Unwinding the amplituhedron in binary

Abstract

We present new, fundamentally combinatorial and topological characterizations of the amplituhedron. Upon projecting external data through the amplituhedron, the resulting configuration of points has a specified (and maximal) generalized “winding number”. Equivalently, the amplituhedron can be fully described in binary: canonical projections of the geometry down to one dimension have a specified (and maximal) number of “sign flips” of the projected data. The locality and unitarity of scattering amplitudes are easily derived as elementary consequences of this binary code. Minimal winding defines a natural “dual” of the amplituhedron. This picture gives us an avatar of the amplituhedron purely in the configuration space of points in vector space (momentum-twistor space in the physics), a new interpretation of the canonical amplituhedron form, and a direct bosonic understanding of the scattering super-amplitude in planar N = 4 SYM as a differential form on the space of physical kinematical data.

Authors:

Arkani-Hamed, Nima ^[1]; Thomas, Hugh ^[2]; Trnka, Jaroslav ^[3]

Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
Univ. of Montreal, Quebec (Canada). Dept. de Mathematiques
Univ. of California, Davis, CA (United States). Center for Quantum Mathematics and Physics (QMAP), Dept. of Physics

Publication Date:: Wed Jan 03 00:00:00 EST 2018

Research Org.:: Institute for Advanced Study, Princeton, NJ (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1502437

Grant/Contract Number:: SC0009988

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: 2018; Journal Issue: 1; 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; Supersymmetric Gauge Theory

Citation Formats


                    Arkani-Hamed, Nima, Thomas, Hugh, and Trnka, Jaroslav. Unwinding the amplituhedron in binary.  United States: N. p., 2018. 
Web.  doi:10.1007/jhep01(2018)016.

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                    Arkani-Hamed, Nima, Thomas, Hugh, & Trnka, Jaroslav. Unwinding the amplituhedron in binary.  United States.  https://doi.org/10.1007/jhep01(2018)016

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                    Arkani-Hamed, Nima, Thomas, Hugh, and Trnka, Jaroslav. Wed .  
"Unwinding the amplituhedron in binary".  United States.  https://doi.org/10.1007/jhep01(2018)016.  https://www.osti.gov/servlets/purl/1502437.

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@article{osti_1502437,

  title        = {Unwinding the amplituhedron in binary},

  author       = {Arkani-Hamed, Nima and Thomas, Hugh and Trnka, Jaroslav},

  abstractNote = {We present new, fundamentally combinatorial and topological characterizations of the amplituhedron. Upon projecting external data through the amplituhedron, the resulting configuration of points has a specified (and maximal) generalized “winding number”. Equivalently, the amplituhedron can be fully described in binary: canonical projections of the geometry down to one dimension have a specified (and maximal) number of “sign flips” of the projected data. The locality and unitarity of scattering amplitudes are easily derived as elementary consequences of this binary code. Minimal winding defines a natural “dual” of the amplituhedron. This picture gives us an avatar of the amplituhedron purely in the configuration space of points in vector space (momentum-twistor space in the physics), a new interpretation of the canonical amplituhedron form, and a direct bosonic understanding of the scattering super-amplitude in planar N = 4 SYM as a differential form on the space of physical kinematical data.},

  doi          = {10.1007/jhep01(2018)016},

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

  number       = 1,

  volume       = 2018,

  place        = {United States},

  year         = {Wed Jan 03 00:00:00 EST 2018},

  month        = {Wed Jan 03 00:00:00 EST 2018}

}

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Works referenced in this record:

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Arkani-Hamed, Nima; Trnka, Jaroslav
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The amplituhedron from momentum twistor diagrams
journal, February 2015

Bai, Yuntao; He, Song
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Golden, J. K.; Goncharov, A. B.; Spradlin, M.
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The correlahedron
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Eden, Burkhard; Heslop, Paul; Mason, Lionel
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journal, May 2013

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Works referencing / citing this record:

Δ-algebra and scattering amplitudes
journal, February 2019

Cachazo, Freddy; Early, Nick; Guevara, Alfredo
Journal of High Energy Physics, Vol. 2019, Issue 2
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Bolshov, A. E.; Bork, L. V.; Onishchenko, A. I.
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Ferro, Livia; Łukowski, Tomasz; Parisi, Matteo
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Goncharov, Y. O.; Vasiliev, M. A.
Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 38
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Accordiohedra as positive geometries for generic scalar field theories
journal, November 2019

Aneesh, P. B.; Jagadale, Mrunmay; Kalyanapuram, Nikhil
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Prlina, Igor; Spradlin, Marcus; Stankowicz, James
arXiv
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Scattering amplitudes as multi-particle higher-spin charges in the correspondence space
text, January 2018

Goncharov, Y. O.; Vasiliev, M. A.
arXiv
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All-loop cuts from the Amplituhedron
text, January 2019

Langer, Cameron; Srikant, Akshay Yelleshpur
arXiv
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The totally nonnegative Grassmannian is a ball
text, January 2017

Galashin, Pavel; Karp, Steven N.; Lam, Thomas
arXiv
DOI: 10.48550/arxiv.1707.02010

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Similar Records

Title: Unwinding the amplituhedron in binary

Abstract

Citation Formats

Multi-loop positivity of the planar N $$ \mathcal{N} $$ = 4 SYM six-point amplitude journal, February 2017

Perturbative Gauge Theory as a String Theory in Twistor Space journal, October 2004

Into the amplituhedron journal, December 2014

The amplituhedron and the one-loop Grassmannian measure journal, January 2016

Positive amplitudes in the amplituhedron journal, August 2015

Classical Polylogarithms for Amplitudes and Wilson Loops journal, October 2010

Amplituhedron Cells and Stanley Symmetric Functions journal, March 2016

Tree-level scattering amplitudes from the amplituhedron journal, May 2017

Landau singularities from the amplituhedron journal, June 2017

The Amplituhedron journal, October 2014

𝒩 = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals journal, October 2008

Anatomy of the amplituhedron journal, March 2015

Positive geometries and canonical forms journal, November 2017

The amplituhedron from momentum twistor diagrams journal, February 2015

Motivic amplitudes and cluster coordinates journal, January 2014

The correlahedron journal, September 2017

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

ABJM amplitudes and the positive orthogonal Grassmannian journal, February 2014

Towards the amplituhedron volume journal, March 2016

Grassmannian Geometry of Scattering Amplitudes book, May 2016

Δ-algebra and scattering amplitudes journal, February 2019

The all-loop conjecture for integrands of reggeon amplitudes in N = 4 $$ \mathcal{N}=4 $$ SYM journal, June 2018

Amplituhedron meets Jeffrey–Kirwan residue journal, December 2018

Scattering amplitudes as multi-particle higher-spin charges in the correspondence space journal, August 2019

Accordiohedra as positive geometries for generic scalar field theories journal, November 2019

All-Helicity Symbol Alphabets from Unwound Amplituhedra text, January 2017

Boundaries of Amplituhedra and NMHV Symbol Alphabets at Two Loops text, January 2017

Scattering amplitudes as multi-particle higher-spin charges in the correspondence space text, January 2018

All-loop cuts from the Amplituhedron text, January 2019

The totally nonnegative Grassmannian is a ball text, January 2017

Multi-loop positivity of the planar N $$ \mathcal{N} $$ = 4 SYM six-point amplitude
journal, February 2017

Perturbative Gauge Theory as a String Theory in Twistor Space
journal, October 2004

Into the amplituhedron
journal, December 2014

The amplituhedron and the one-loop Grassmannian measure
journal, January 2016

Positive amplitudes in the amplituhedron
journal, August 2015

Classical Polylogarithms for Amplitudes and Wilson Loops
journal, October 2010

Amplituhedron Cells and Stanley Symmetric Functions
journal, March 2016

Tree-level scattering amplitudes from the amplituhedron
journal, May 2017

Landau singularities from the amplituhedron
journal, June 2017

The Amplituhedron
journal, October 2014

𝒩 = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
journal, October 2008

Anatomy of the amplituhedron
journal, March 2015

Positive geometries and canonical forms
journal, November 2017

The amplituhedron from momentum twistor diagrams
journal, February 2015

Motivic amplitudes and cluster coordinates
journal, January 2014

The correlahedron
journal, September 2017

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

ABJM amplitudes and the positive orthogonal Grassmannian
journal, February 2014

Towards the amplituhedron volume
journal, March 2016

Grassmannian Geometry of Scattering Amplitudes
book, May 2016

Δ-algebra and scattering amplitudes
journal, February 2019

The all-loop conjecture for integrands of reggeon amplitudes in N = 4 $$ \mathcal{N}=4 $$ SYM
journal, June 2018

Amplituhedron meets Jeffrey–Kirwan residue
journal, December 2018

Scattering amplitudes as multi-particle higher-spin charges in the correspondence space
journal, August 2019

Accordiohedra as positive geometries for generic scalar field theories
journal, November 2019

All-Helicity Symbol Alphabets from Unwound Amplituhedra
text, January 2017

Boundaries of Amplituhedra and NMHV Symbol Alphabets at Two Loops
text, January 2017

Scattering amplitudes as multi-particle higher-spin charges in the correspondence space
text, January 2018

All-loop cuts from the Amplituhedron
text, January 2019

The totally nonnegative Grassmannian is a ball
text, January 2017