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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:
 [1];  [2];  [3]
  1. Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
  2. Univ. of Montreal, Quebec (Canada). Dept. de Mathematiques
  3. Univ. of California, Davis, CA (United States). Center for Quantum Mathematics and Physics (QMAP), Dept. of Physics
Publication Date:
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.
Arkani-Hamed, Nima, Thomas, Hugh, & Trnka, Jaroslav. Unwinding the amplituhedron in binary. United States. doi:https://doi.org/10.1007/jhep01(2018)016
Arkani-Hamed, Nima, Thomas, Hugh, and Trnka, Jaroslav. Wed . "Unwinding the amplituhedron in binary". United States. doi:https://doi.org/10.1007/jhep01(2018)016. https://www.osti.gov/servlets/purl/1502437.
@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 = {2018},
month = {1}
}

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Cited by: 26 works
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    Works referencing / citing this record:

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