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

doi:https://doi.org/10.1007/JHEP12(2014)181

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:

Elvang, Henriette ^[1]; Huang, Yu-tin ^[2]; Keeler, Cynthia ^[1]; Lam, Thomas ^[3]; Olson, Timothy M. ^[1]; Roland, Samuel B. ^[1]; Speyer, David E. ^[3]

Univ. of Michigan, Ann Arbor, MI (United States). Michigan Center for Theoretical Physics and Randall Lab. of Physics, Dept. of Physics
National Taiwan Univ., Taipei (Taiwan). Dept. of Physics and Astronomy
Univ. of Michigan, Ann Arbor, MI (United States). Dept. of Mathematics

Publication Date:: 2014-12-31

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.

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                    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

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                    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.

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@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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Works referenced in this record:

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Amplitudes of 3d Yang Mills theory
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Dual superconformal invariance, momentum twistors and Grassmannians
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Uplifting amplitudes in special kinematics
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Tree-level recursion relation and dual superconformal symmetry of the ABJM theory
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Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory
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One-loop amplitudes in 𝒩 = 4 super Yang-Mills and anomalous dual conformal symmetry
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Engelund, Oluf Tang; Roiban, Radu
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Integral Formula for Supersymmetric Scattering Amplitudes in Three Dimensions
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Huang, Yu-tin; Lee, Sangmin
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Yangian-Invariant Scattering Amplitudes in Supersymmetric Chern-Simons Theory
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Lee, Sangmin
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Positroid stratification of orthogonal Grassmannian and ABJM amplitudes
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Kim, Joonho; Lee, Sangmin
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The multidimensional cube recurrence
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Henriques, Andre; Speyer, David E.
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All tree-level amplitudes in 𝒩 = 4 SYM
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Drummond, J. M.; Henn, J. M.
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Scattering amplitudes and BCFW recursion in twistor space
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Mason, Lionel; Skinner, David
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Dual conformal constraints and infrared equations from global residue theorems in $ \mathcal{N} = 4 $ SYM theory
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Brödel, Johannes; He, Song
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𝒩 = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
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Aharony, Ofer; Bergman, Oren; Jafferis, Daniel Louis
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The Grassmannian origin of dual superconformal invariance
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Arkani-Hamed, Nima; Cachazo, Freddy; Cheung, Clifford
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ABJM amplitudes and the positive orthogonal Grassmannian
journal, February 2014

Huang, Yu-tin; Wen, CongKao
Journal of High Energy Physics, Vol. 2014, Issue 2
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Eliminating spurious poles from gauge-theoretic amplitudes
journal, May 2013

Hodges, Andrew
Journal of High Energy Physics, Vol. 2013, Issue 5
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Twistor-strings, Grassmannians and leading singularities
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Bullimore, Mathew; Mason, Lionel; Skinner, David
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Works referencing / citing this record:

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

Frassek, Rouven; Meidinger, David; Nandan, Dhritiman
Journal of High Energy Physics, Vol. 2016, Issue 1
https://doi.org/10.1007/jhep01(2016)182

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

Bork, L. V.; Onishchenko, A. I.
Journal of High Energy Physics, Vol. 2017, Issue 4
https://doi.org/10.1007/jhep04(2017)019

Logarithmic singularities and maximally supersymmetric amplitudes
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Bern, Zvi; Herrmann, Enrico; Litsey, Sean
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https://doi.org/10.1007/jhep06(2015)202

Evidence for a nonplanar amplituhedron
journal, June 2016

Bern, Zvi; Herrmann, Enrico; Litsey, Sean
Journal of High Energy Physics, Vol. 2016, Issue 6
https://doi.org/10.1007/jhep06(2016)098

Orientations of BCFW charts on the Grassmannian
journal, August 2015

Olson, Timothy M.
Journal of High Energy Physics, Vol. 2015, Issue 8
https://doi.org/10.1007/jhep08(2015)120

Gravity on-shell diagrams
journal, November 2016

Herrmann, Enrico; Trnka, Jaroslav
Journal of High Energy Physics, Vol. 2016, Issue 11
https://doi.org/10.1007/jhep11(2016)136

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

Benincasa, Paolo; Gordo, David
Journal of High Energy Physics, Vol. 2017, Issue 11
https://doi.org/10.1007/jhep11(2017)192

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

Bork, L. V.; Onishchenko, A. I.
Journal of High Energy Physics, Vol. 2016, Issue 12
https://doi.org/10.1007/jhep12(2016)076

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

Rao, Junjie
Journal of High Energy Physics, Vol. 2017, Issue 12
https://doi.org/10.1007/jhep12(2017)147

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

Bourjaily, Jacob L.; Herrmann, Enrico; Langer, Cameron
Journal of High Energy Physics, Vol. 2019, Issue 12
https://doi.org/10.1007/jhep12(2019)073

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

Chen, Baoyi; Chen, Gang; Cheung, Yeuk-Kwan E.
The European Physical Journal C, Vol. 78, Issue 2
https://doi.org/10.1140/epjc/s10052-018-5629-z

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Similar Records

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

Abstract

Citation Formats

Finite-component field representations of the conformal group journal, June 1969

Dual superconformal symmetry of scattering amplitudes in super-Yang–Mills theory journal, March 2010

𝒩 = 5, 6 superconformal Chern-Simons theories and M2-branes on orbifolds journal, September 2008

Amplitudes of 3d Yang Mills theory journal, January 2013

Dual superconformal invariance, momentum twistors and Grassmannians journal, November 2009

Uplifting amplitudes in special kinematics journal, October 2012

The Amplituhedron journal, October 2014

Tree-level recursion relation and dual superconformal symmetry of the ABJM theory journal, March 2011

Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory journal, August 2013

A note on polytopes for scattering amplitudes journal, April 2012

One-loop amplitudes in 𝒩 = 4 super Yang-Mills and anomalous dual conformal symmetry journal, August 2009

Wave Equations in Conformal Space journal, April 1936

A duality for the S matrix journal, March 2010

A twistor string for the ABJ(M) theory journal, June 2014

Integral Formula for Supersymmetric Scattering Amplitudes in Three Dimensions journal, November 2012

Unification of residues and Grassmannian dualities journal, January 2011

Amplitude for n -Gluon Scattering journal, June 1986

A current algebra for some gauge theory amplitudes journal, November 1988

Yangian-Invariant Scattering Amplitudes in Supersymmetric Chern-Simons Theory journal, October 2010

Positroid stratification of orthogonal Grassmannian and ABJM amplitudes journal, September 2014

The multidimensional cube recurrence journal, February 2010

All tree-level amplitudes in 𝒩 = 4 SYM journal, April 2009

Scattering amplitudes and BCFW recursion in twistor space journal, January 2010

Dual conformal constraints and infrared equations from global residue theorems in $ \mathcal{N} = 4 $ SYM theory journal, June 2010

𝒩 = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals journal, October 2008

The Grassmannian origin of dual superconformal invariance journal, March 2010

Massless, Euclidean Quantum Electrodynamics on the 5-Dimensional Unit Hypersphere journal, December 1972

ABJM amplitudes and the positive orthogonal Grassmannian journal, February 2014

Eliminating spurious poles from gauge-theoretic amplitudes journal, May 2013

Twistor-strings, Grassmannians and leading singularities journal, March 2010

Dual conformal symmetry of 1-loop NMHV amplitudes in $ \mathcal{N} = 4 $ SYM theory journal, March 2010

Massless, Euclidean Quantum Electrodynamics on the 5-Dimensional Unit Hypersphere journal, June 1973

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

Finite-component field representations of the conformal group
journal, June 1969

Dual superconformal symmetry of scattering amplitudes in super-Yang–Mills theory
journal, March 2010

𝒩 = 5, 6 superconformal Chern-Simons theories and M2-branes on orbifolds
journal, September 2008

Amplitudes of 3d Yang Mills theory
journal, January 2013

Dual superconformal invariance, momentum twistors and Grassmannians
journal, November 2009

Uplifting amplitudes in special kinematics
journal, October 2012

The Amplituhedron
journal, October 2014

Tree-level recursion relation and dual superconformal symmetry of the ABJM theory
journal, March 2011

Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory
journal, August 2013

A note on polytopes for scattering amplitudes
journal, April 2012

One-loop amplitudes in 𝒩 = 4 super Yang-Mills and anomalous dual conformal symmetry
journal, August 2009

Wave Equations in Conformal Space
journal, April 1936

A duality for the S matrix
journal, March 2010

A twistor string for the ABJ(M) theory
journal, June 2014

Integral Formula for Supersymmetric Scattering Amplitudes in Three Dimensions
journal, November 2012

Unification of residues and Grassmannian dualities
journal, January 2011

Amplitude for $n$ -Gluon Scattering
journal, June 1986

A current algebra for some gauge theory amplitudes
journal, November 1988

Yangian-Invariant Scattering Amplitudes in Supersymmetric Chern-Simons Theory
journal, October 2010

Positroid stratification of orthogonal Grassmannian and ABJM amplitudes
journal, September 2014

The multidimensional cube recurrence
journal, February 2010

All tree-level amplitudes in 𝒩 = 4 SYM
journal, April 2009

Scattering amplitudes and BCFW recursion in twistor space
journal, January 2010

Dual conformal constraints and infrared equations from global residue theorems in $ \mathcal{N} = 4 $ SYM theory
journal, June 2010

𝒩 = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
journal, October 2008

The Grassmannian origin of dual superconformal invariance
journal, March 2010

Massless, Euclidean Quantum Electrodynamics on the 5-Dimensional Unit Hypersphere
journal, December 1972

ABJM amplitudes and the positive orthogonal Grassmannian
journal, February 2014

Eliminating spurious poles from gauge-theoretic amplitudes
journal, May 2013

Twistor-strings, Grassmannians and leading singularities
journal, March 2010

Dual conformal symmetry of 1-loop NMHV amplitudes in $ \mathcal{N} = 4 $ SYM theory
journal, March 2010

Massless, Euclidean Quantum Electrodynamics on the 5-Dimensional Unit Hypersphere
journal, June 1973

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