Unwinding the amplituhedron in binary

Journal Article · Wed Jan 03 00:00:00 EST 2018 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep01(2018)016· OSTI ID:1502437

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

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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

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.

• Research Organization: Institute for Advanced Study, Princeton, NJ (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: SC0009988
• OSTI ID: 1502437
• Journal Information: Journal of High Energy Physics (Online), Vol. 2018, Issue 1; ISSN 1029-8479
• Publisher: Springer Berlin
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Scattering Amplitudes
Supersymmetric Gauge Theory