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

Abstract

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.

Authors:
 [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
Publication Date:
Research Org.:
Univ. of Michigan, Ann Arbor, MI (United States)
Sponsoring Org.:
USDOE; National Science Foundation (NSF)
OSTI Identifier:
1440977
Grant/Contract Number:  
SC0011719; PHY-0953232; FG02-95ER40899; DMS-1160726; F031543
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
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; Scattering Amplitudes; Supersymmetric gauge theory; Differential and Algebraic Geometry

Citation Formats

Elvang, Henriette, Huang, Yu-tin, Keeler, Cynthia, Lam, Thomas, Olson, Timothy M., Roland, Samuel B., and Speyer, David E. Grassmannians for scattering amplitudes in 4d $\mathcal{N}=4 $ SYM and 3d ABJM. United States: N. p., 2014. Web. doi:10.1007/JHEP12(2014)181.
Elvang, Henriette, Huang, Yu-tin, Keeler, Cynthia, Lam, Thomas, Olson, Timothy M., Roland, Samuel B., & Speyer, David E. Grassmannians for scattering amplitudes in 4d $\mathcal{N}=4 $ SYM and 3d ABJM. United States. https://doi.org/10.1007/JHEP12(2014)181
Elvang, Henriette, Huang, Yu-tin, Keeler, Cynthia, Lam, Thomas, Olson, Timothy M., Roland, Samuel B., and Speyer, David E. Wed . "Grassmannians for scattering amplitudes in 4d $\mathcal{N}=4 $ SYM and 3d ABJM". United States. https://doi.org/10.1007/JHEP12(2014)181. https://www.osti.gov/servlets/purl/1440977.
@article{osti_1440977,
title = {Grassmannians for scattering amplitudes in 4d $\mathcal{N}=4 $ SYM and 3d ABJM},
author = {Elvang, Henriette and Huang, Yu-tin and Keeler, Cynthia and Lam, Thomas and Olson, Timothy M. and Roland, Samuel B. and Speyer, David E.},
abstractNote = {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.},
doi = {10.1007/JHEP12(2014)181},
url = {https://www.osti.gov/biblio/1440977}, journal = {Journal of High Energy Physics (Online)},
issn = {1029-8479},
number = 12,
volume = 2014,
place = {United States},
year = {2014},
month = {12}
}

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Free Publicly Available Full Text
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Cited by: 13 works
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Works referenced in this record:

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    Works referencing / citing this record:

    On-shell diagrams, Graßmannians and integrability for form factors
    journal, January 2016


    Wilson lines, Grassmannians and gauge invariant off-shell amplitudes in N = 4 $$ \mathcal{N}=4 $$ SYM
    journal, April 2017


    Logarithmic singularities and maximally supersymmetric amplitudes
    journal, June 2015


    Evidence for a nonplanar amplituhedron
    journal, June 2016


    Orientations of BCFW charts on the Grassmannian
    journal, August 2015


    Gravity on-shell diagrams
    journal, November 2016


    On-shell diagrams and the geometry of planar N < 4 $$ \mathcal{N}<4 $$ SYM theories
    journal, November 2017


    Grassmannians and form factors with q 2 = 0 in N $$ \mathcal{N} $$ =4 SYM theory
    journal, December 2016


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


    Prescriptive unitarity for non-planar six-particle amplitudes at two loops
    journal, December 2019


    Top-forms of leading singularities in nonplanar multi-loop amplitudes
    journal, February 2018