Grassmannians for scattering amplitudes in 4d N=4 SYM and 3d ABJM

Henriette Elvang, Yu Tin Huang, Cynthia Keeler, Thomas Lam, Timothy M. Olson, Samuel B. Roland, David E. Speyer

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

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. 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.

Original languageEnglish (US)
Article number181
Pages (from-to)1-51
Number of pages51
JournalJournal of High Energy Physics
Volume2014
Issue number12
DOIs
StatePublished - Jan 1 2014
Externally publishedYes

Fingerprint

Yang-Mills theory
scattering amplitude
momentum
formulations
equivalence
poles
theorems

Keywords

  • Differential and Algebraic Geometry
  • Scattering Amplitudes
  • Supersymmetric gauge theory

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Cite this

Elvang, H., Huang, Y. T., Keeler, C., Lam, T., Olson, T. M., Roland, S. B., & Speyer, D. E. (2014). Grassmannians for scattering amplitudes in 4d N=4 SYM and 3d ABJM. Journal of High Energy Physics, 2014(12), 1-51. [181]. https://doi.org/10.1007/JHEP12(2014)181

Grassmannians for scattering amplitudes in 4d N=4 SYM and 3d ABJM. / Elvang, Henriette; Huang, Yu Tin; Keeler, Cynthia; Lam, Thomas; Olson, Timothy M.; Roland, Samuel B.; Speyer, David E.

In: Journal of High Energy Physics, Vol. 2014, No. 12, 181, 01.01.2014, p. 1-51.

Research output: Contribution to journalArticle

Elvang, H, Huang, YT, Keeler, C, Lam, T, Olson, TM, Roland, SB & Speyer, DE 2014, 'Grassmannians for scattering amplitudes in 4d N=4 SYM and 3d ABJM', Journal of High Energy Physics, vol. 2014, no. 12, 181, pp. 1-51. https://doi.org/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 N=4 SYM and 3d ABJM. In: Journal of High Energy Physics. 2014 ; Vol. 2014, No. 12. pp. 1-51.
@article{001ac1b9d09548909746eb60e9d1bfd6,
title = "Grassmannians for scattering amplitudes in 4d N=4 SYM and 3d ABJM",
abstract = "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. 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.",
keywords = "Differential and Algebraic Geometry, Scattering Amplitudes, Supersymmetric gauge theory",
author = "Henriette Elvang and Huang, {Yu Tin} and Cynthia Keeler and Thomas Lam and Olson, {Timothy M.} and Roland, {Samuel B.} and Speyer, {David E.}",
year = "2014",
month = "1",
day = "1",
doi = "10.1007/JHEP12(2014)181",
language = "English (US)",
volume = "2014",
pages = "1--51",
journal = "Journal of High Energy Physics",
issn = "1029-8479",
publisher = "Springer Verlag",
number = "12",

}

TY - JOUR

T1 - Grassmannians for scattering amplitudes in 4d N=4 SYM and 3d ABJM

AU - Elvang, Henriette

AU - Huang, Yu Tin

AU - Keeler, Cynthia

AU - Lam, Thomas

AU - Olson, Timothy M.

AU - Roland, Samuel B.

AU - Speyer, David E.

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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. 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.

AB - 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. 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.

KW - Differential and Algebraic Geometry

KW - Scattering Amplitudes

KW - Supersymmetric gauge theory

UR - http://www.scopus.com/inward/record.url?scp=84920477324&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84920477324&partnerID=8YFLogxK

U2 - 10.1007/JHEP12(2014)181

DO - 10.1007/JHEP12(2014)181

M3 - Article

AN - SCOPUS:84920477324

VL - 2014

SP - 1

EP - 51

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1029-8479

IS - 12

M1 - 181

ER -