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Title: Grassmannians for scattering amplitudes in 4d $$\mathcal{N}=4 $$ SYM and 3d ABJM

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2];  [1];  [3];  [1];  [1];  [3]
  1. Univ. of Michigan, Ann Arbor, MI (United States). Michigan Center for Theoretical Physics and Randall Lab. of Physics, Dept. of Physics
  2. National Taiwan Univ., Taipei (Taiwan). Dept. of Physics and Astronomy
  3. Univ. of Michigan, Ann Arbor, MI (United States). Dept. of Mathematics
+ Show Author Affiliations

Scattering amplitudes in 4d N=4 super Yang-Mills theory (SYM) can be described by Grassmannian contour integrals whose form depends on whether the external data is encoded in momentum space, twistor space, or momentum twistor space. Here, after a pedagogical review, we present a new, streamlined proof of the equivalence of the three integral formulations. A similar strategy allows us to derive a new Grassmannian integral for 3d N = 6 ABJM theory amplitudes in momentum twistor space: it is a contour integral in an orthogonal Grassmannian with the novel property that the internal metric depends on the external data. The result can be viewed as a central step towards developing an amplituhedron formulation for ABJM amplitudes. Various properties of Grassmannian integrals are examined, including boundary properties, pole structure, and a homological interpretation of the global residue theorems for N = 4 SYM.

Research Organization:
Univ. of Michigan, Ann Arbor, MI (United States)
Sponsoring Organization:
USDOE; National Science Foundation (NSF)
Grant/Contract Number:
SC0011719; PHY-0953232; FG02-95ER40899; DMS-1160726; F031543
OSTI ID:
1440977
Journal Information:
Journal of High Energy Physics (Online), Vol. 2014, Issue 12; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 23 works
Citation information provided by
Web of Science

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Cited By (9)

On-shell diagrams, Graßmannians and integrability for form factors journal January 2016
Orientations of BCFW charts on the Grassmannian journal August 2015
Positivity, Grassmannian geometry and simplex-like structures of scattering amplitudes journal December 2017
Top-forms of leading singularities in nonplanar multi-loop amplitudes journal February 2018
Orientations of BCFW Charts on the Grassmannian preprint January 2014
Logarithmic Singularities and Maximally Supersymmetric Amplitudes preprint January 2014
Evidence for a Nonplanar Amplituhedron text January 2015
Gravity On-shell Diagrams text January 2016
Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops text January 2019

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Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Scattering Amplitudes
Supersymmetric gauge theory
Differential and Algebraic Geometry