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Title: Anatomy of the amplituhedron

Abstract

We initiate a comprehensive investigation of the geometry of the amplituhedron, a recently found geometric object whose volume calculates the integrand of scattering amplitudes in planar \( \mathcal{N}=4 \) SYM theory. We do so by introducing and studying its stratification, focusing on four-point amplitudes. The new stratification exhibits interesting combinatorial properties and positivity is neatly captured by permutations. As explicit examples, we find all boundaries for the two and three loop amplitudes and related geometries. We recover the stratifications of some of these geometries from the singularities of the corresponding integrands, providing a non-trivial test of the amplituhedron/scattering amplitude correspondence. We finally introduce a deformation of the stratification with remarkably simple topological properties.

Authors:
 [1];  [1];  [1];  [2]
  1. Durham Univ. (United Kingdom)
  2. California Inst. of Technology (CalTech), Pasadena, CA (United States)
Publication Date:
Research Org.:
California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); UK Science and Technology Facilities Council (STFC)
OSTI Identifier:
1596492
Grant/Contract Number:  
SC0011632; FG03-92ER40701
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: 2015; Journal Issue: 3; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Supersymmetric gauge theory; Scattering Amplitudes

Citation Formats

Franco, Sebastián, Galloni, Daniele, Mariotti, Alberto, and Trnka, Jaroslav. Anatomy of the amplituhedron. United States: N. p., 2015. Web. doi:10.1007/JHEP03(2015)128.
Franco, Sebastián, Galloni, Daniele, Mariotti, Alberto, & Trnka, Jaroslav. Anatomy of the amplituhedron. United States. https://doi.org/10.1007/JHEP03(2015)128
Franco, Sebastián, Galloni, Daniele, Mariotti, Alberto, and Trnka, Jaroslav. Tue . "Anatomy of the amplituhedron". United States. https://doi.org/10.1007/JHEP03(2015)128. https://www.osti.gov/servlets/purl/1596492.
@article{osti_1596492,
title = {Anatomy of the amplituhedron},
author = {Franco, Sebastián and Galloni, Daniele and Mariotti, Alberto and Trnka, Jaroslav},
abstractNote = {We initiate a comprehensive investigation of the geometry of the amplituhedron, a recently found geometric object whose volume calculates the integrand of scattering amplitudes in planar \( \mathcal{N}=4 \) SYM theory. We do so by introducing and studying its stratification, focusing on four-point amplitudes. The new stratification exhibits interesting combinatorial properties and positivity is neatly captured by permutations. As explicit examples, we find all boundaries for the two and three loop amplitudes and related geometries. We recover the stratifications of some of these geometries from the singularities of the corresponding integrands, providing a non-trivial test of the amplituhedron/scattering amplitude correspondence. We finally introduce a deformation of the stratification with remarkably simple topological properties.},
doi = {10.1007/JHEP03(2015)128},
journal = {Journal of High Energy Physics (Online)},
number = 3,
volume = 2015,
place = {United States},
year = {Tue Mar 24 00:00:00 EDT 2015},
month = {Tue Mar 24 00:00:00 EDT 2015}
}

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Cited by: 40 works
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Works referencing / citing this record:

Four-dimensional ambitwistor strings and form factors of local and Wilson line operators
journal, June 2018


Top-forms of leading singularities in nonplanar multi-loop amplitudes
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All-loop cuts from the Amplituhedron
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Positivity, Grassmannian geometry and simplex-like structures of scattering amplitudes
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Emergent unitarity from the amplituhedron
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