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Title: Into the amplituhedron

Abstract

We initiate an exploration of the physics and geometry of the amplituhedron, starting with the simplest case of the integrand for four-particle scattering in planar \( \mathcal{N}=4 \) SYM. We show how the textbook structure of the unitarity double-cut follows from the positive geometry. We also use the geometry to expose the behavior of the multicollinear limit, providing a direct motivation for studying the logarithm of the amplitude. In addition to computing the two and three-loop integrands, we explore various lower-dimensional faces of the amplituhedron, thereby computing non-trivial cuts of the integrand to all loop orders.

Authors:
 [1];  [2]
  1. Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
  2. California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
Publication Date:
Research Org.:
Institute for Advanced Study, Princeton, NJ (United States); Harvard Univ., Cambridge, MA (United States); California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)
OSTI Identifier:
1598502
Grant/Contract Number:  
SC0009988; FG02-91ER40654; FG03-92ER40701; PHY-0756966
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: 2014; Journal Issue: 12; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; supersymmetry: 4; geometry; scattering; unitarity; supersymmetric gauge theory; scattering amplitudes

Citation Formats

Arkani-Hamed, Nima, and Trnka, Jaroslav. Into the amplituhedron. United States: N. p., 2014. Web. doi:10.1007/JHEP12(2014)182.
Arkani-Hamed, Nima, & Trnka, Jaroslav. Into the amplituhedron. United States. https://doi.org/10.1007/JHEP12(2014)182
Arkani-Hamed, Nima, and Trnka, Jaroslav. Wed . "Into the amplituhedron". United States. https://doi.org/10.1007/JHEP12(2014)182. https://www.osti.gov/servlets/purl/1598502.
@article{osti_1598502,
title = {Into the amplituhedron},
author = {Arkani-Hamed, Nima and Trnka, Jaroslav},
abstractNote = {We initiate an exploration of the physics and geometry of the amplituhedron, starting with the simplest case of the integrand for four-particle scattering in planar \( \mathcal{N}=4 \) SYM. We show how the textbook structure of the unitarity double-cut follows from the positive geometry. We also use the geometry to expose the behavior of the multicollinear limit, providing a direct motivation for studying the logarithm of the amplitude. In addition to computing the two and three-loop integrands, we explore various lower-dimensional faces of the amplituhedron, thereby computing non-trivial cuts of the integrand to all loop orders.},
doi = {10.1007/JHEP12(2014)182},
journal = {Journal of High Energy Physics (Online)},
number = 12,
volume = 2014,
place = {United States},
year = {Wed Dec 31 00:00:00 EST 2014},
month = {Wed Dec 31 00:00:00 EST 2014}
}

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Works referenced in this record:

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Works referencing / citing this record:

UV cancellations in gravity loop integrands
journal, February 2019

  • Herrmann, Enrico; Trnka, Jaroslav
  • Journal of High Energy Physics, Vol. 2019, Issue 2
  • DOI: 10.1007/jhep02(2019)084

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

  • Bolshov, A. E.; Bork, L. V.; Onishchenko, A. I.
  • Journal of High Energy Physics, Vol. 2018, Issue 6
  • DOI: 10.1007/jhep06(2018)129

Heptagons from the Steinmann Cluster Bootstrap
text, January 2017

  • Dixon, Lance J.; Drummond, James; Harrington, Thomas
  • Deutsches Elektronen-Synchrotron, DESY, Hamburg
  • DOI: 10.3204/pubdb-2017-00889

Accordiohedra as positive geometries for generic scalar field theories
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On-shell diagrams for N $$ \mathcal{N} $$ = 8 supergravity amplitudes
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  • Heslop, Paul; Lipstein, Arthur E.
  • Journal of High Energy Physics, Vol. 2016, Issue 6
  • DOI: 10.1007/jhep06(2016)069

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


The Sklyanin bracket and cluster adjacency at all multiplicity
journal, March 2019

  • Golden, John; McLeod, Andrew J.; Spradlin, Marcus
  • Journal of High Energy Physics, Vol. 2019, Issue 3
  • DOI: 10.1007/jhep03(2019)195

Amplituhedron meets Jeffrey–Kirwan residue
journal, December 2018

  • Ferro, Livia; Łukowski, Tomasz; Parisi, Matteo
  • Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 4
  • DOI: 10.1088/1751-8121/aaf3c3

Properties of scattering forms and their relation to associahedra
journal, March 2018

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Non-planar on-shell diagrams
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Six-Gluon Amplitudes in Planar ${\cal N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
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The double pentaladder integral to all ordersC
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Orientations of BCFW Charts on the Grassmannian
preprint, January 2014


Logarithmic Singularities and Maximally Supersymmetric Amplitudes
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Non-Planar On-Shell Diagrams
preprint, January 2015


Local Integrand Representations of All Two-Loop Amplitudes in Planar SYM
text, January 2015


Evidence for a Nonplanar Amplituhedron
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Gravity On-shell Diagrams
text, January 2016


Heptagons from the Steinmann Cluster Bootstrap
text, January 2016


Prescriptive Unitarity
text, January 2017


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


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


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


The Double Pentaladder Integral to All Orders
text, January 2018


All-loop cuts from the Amplituhedron
text, January 2019


The Sklyanin Bracket and Cluster Adjacency at All Multiplicity
text, January 2019