The S matrix of 6D super Yang-Mills and maximal supergravity from rational maps

doi:10.1007/jhep09(2018)125

Title: The S matrix of 6D super Yang-Mills and maximal supergravity from rational maps

Abstract

We present new formulas for n-particle tree-level scattering amplitudes of six-dimensional N = (1,1) super Yang-Mills (SYM) and N = (2,2) supergravity (SUGRA). They are written as integrals over the moduli space of certain rational maps localized on the (n – 3)! solutions of the scattering equations. Due to the properties of spinor-helicity variables in six dimensions, the even-n and odd-n formulas are quite different and have to be treated separately. We first propose a manifestly supersymmetric expression for the even-n amplitudes of N = (1,1) SYM theory and perform various consistency checks. By considering soft-gluon limits of the even-n amplitudes, we deduce the form of the rational maps and the integrand for n odd. The odd-n formulas obtained in this way have a new redundancy that is intertwined with the usual SL(2, C) invariance on the Riemann sphere. We also propose an alternative form of the formulas, analogous to the Witten-RSV formulation, and explore its relationship with the symplectic (or Lagrangian) Grassmannian. Since the amplitudes are formulated in a way that manifests double-copy properties, formulas for the six-dimensional N = (2,2) SUGRA amplitudes follow. Furthermore, these six-dimensional results allow us to deduce new formulas for five-dimensional SYM and SUGRAmore »« less

Authors:

Cachazo, Freddy ^[1]; Guevara, Alfredo ^[2]; Heydeman, Matthew ^[3]; Mizera, Sebastian ^[4]; Schwarz, John H. ^[3]; Wen, Congkao ^[5]

Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada); Univ. of Waterloo, Waterloo, ON (Canada); Univ. de Concepcion, Concepcion (Chile)
California Inst. of Technology (CalTech), Pasadena, CA (United States)
Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada); Univ. of Waterloo, Waterloo, ON (Canada)
California Inst. of Technology (CalTech), Pasadena, CA (United States); Queen Mary Univ. of London, London (United Kingdom)

Publication Date:: 2018-09-20

Research Org.:: California Inst. of Technology, Pasadena, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1501468

Grant/Contract Number:: SC0011632

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: 2018; Journal Issue: 9; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Scattering Amplitudes; Field Theories in Higher Dimensions; Supersymmetric Gauge Theory

Citation Formats


                    Cachazo, Freddy, Guevara, Alfredo, Heydeman, Matthew, Mizera, Sebastian, Schwarz, John H., and Wen, Congkao. The S matrix of 6D super Yang-Mills and maximal supergravity from rational maps.  United States: N. p., 2018. 
        Web.  doi:10.1007/jhep09(2018)125.

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                    Cachazo, Freddy, Guevara, Alfredo, Heydeman, Matthew, Mizera, Sebastian, Schwarz, John H., & Wen, Congkao. The S matrix of 6D super Yang-Mills and maximal supergravity from rational maps.  United States.  doi:10.1007/jhep09(2018)125.

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                    Cachazo, Freddy, Guevara, Alfredo, Heydeman, Matthew, Mizera, Sebastian, Schwarz, John H., and Wen, Congkao. Thu .  
        "The S matrix of 6D super Yang-Mills and maximal supergravity from rational maps".  United States.  doi:10.1007/jhep09(2018)125.  https://www.osti.gov/servlets/purl/1501468.

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@article{osti_1501468,

  title        = {The S matrix of 6D super Yang-Mills and maximal supergravity from rational maps},

  author       = {Cachazo, Freddy and Guevara, Alfredo and Heydeman, Matthew and Mizera, Sebastian and Schwarz, John H. and Wen, Congkao},

  abstractNote = {We present new formulas for n-particle tree-level scattering amplitudes of six-dimensional N = (1,1) super Yang-Mills (SYM) and N = (2,2) supergravity (SUGRA). They are written as integrals over the moduli space of certain rational maps localized on the (n – 3)! solutions of the scattering equations. Due to the properties of spinor-helicity variables in six dimensions, the even-n and odd-n formulas are quite different and have to be treated separately. We first propose a manifestly supersymmetric expression for the even-n amplitudes of N = (1,1) SYM theory and perform various consistency checks. By considering soft-gluon limits of the even-n amplitudes, we deduce the form of the rational maps and the integrand for n odd. The odd-n formulas obtained in this way have a new redundancy that is intertwined with the usual SL(2, C) invariance on the Riemann sphere. We also propose an alternative form of the formulas, analogous to the Witten-RSV formulation, and explore its relationship with the symplectic (or Lagrangian) Grassmannian. Since the amplitudes are formulated in a way that manifests double-copy properties, formulas for the six-dimensional N = (2,2) SUGRA amplitudes follow. Furthermore, these six-dimensional results allow us to deduce new formulas for five-dimensional SYM and SUGRA amplitudes, as well as massive amplitudes of four-dimensional N = 4 SYM on the Coulomb branch.},

  doi          = {10.1007/jhep09(2018)125},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 9,

  volume       = 2018,

  place        = {United States},

  year         = {2018},

  month        = {9}

}

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DOI: 10.1007/jhep09(2018)125

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Herderschee, Aidan; Koren, Seth; Trott, Timothy
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journal, March 2019

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Title: The S matrix of 6D super Yang-Mills and maximal supergravity from rational maps

Abstract

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Scattering in three dimensions from rational maps journal, October 2013

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Semi-abelian Z-theory: NLSM+ϕ 3 from the open string journal, August 2017

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Scattering equations and matrices: from Einstein to Yang-Mills, DBI and NLSM journal, July 2015

Symmetries and strings in field theory and gravity journal, April 2011

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A duality for the S matrix journal, March 2010

Spinor helicity and dual conformal symmetry in ten dimensions journal, August 2011

Britto-Cachazo-Feng-Witten–Type Recurrent Relations for Tree Superamplitudes of D = 11 Supergravity journal, January 2017

Tree-level S matrix of Yang-Mills theory journal, July 2004

Unification of residues and Grassmannian dualities journal, January 2011

Amplitude for n -Gluon Scattering journal, June 1986

New relations for gauge-theory amplitudes journal, October 2008

Infrared Photons and Gravitons journal, October 1965

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

Supertwistor space for 6D maximal super Yang-Mills journal, April 2010

Ward Identity and Scattering Amplitudes for Nonlinear Sigma Models journal, February 2018

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Bootstrapping solutions of scattering equations journal, February 2019

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Semi-abelian Z-theory: NLSM+ϕ 3 from the open string
journal, August 2017

Generalized unitarity and six-dimensional helicity
journal, April 2011

From twistor string theory to recursion relations
journal, October 2009

Pions as gluons in higher dimensions
journal, April 2018

Scattering of Massless Particles in Arbitrary Dimensions
journal, October 2014

One-loop corrections from higher dimensional tree amplitudes
journal, August 2016

Superconformal symmetry and maximal supergravity in various dimensions
journal, March 2012

Chiral three-point interactions in 5 and 6 dimensions
journal, October 2012

Amplitudes and spinor-helicity in six dimensions
journal, July 2009

Ambitwistor Strings in Four Dimensions
journal, August 2014

World-volume action of the M-theory five-brane
journal, July 1997

Scattering equations and matrices: from Einstein to Yang-Mills, DBI and NLSM
journal, July 2015

Symmetries and strings in field theory and gravity
journal, April 2011

Two-loop scattering amplitudes from the Riemann sphere
journal, December 2016

Dual conformal properties of six-dimensional maximal super Yang-Mills amplitudes
journal, January 2011

Scattering of massless particles: scalars, gluons and gravitons
journal, July 2014

The action of the (free) (4, 0)-theory
journal, January 2018

Magic identities for conformal four-point integrals
journal, January 2007

New ambitwistor string theories
journal, November 2015

Extensions of theories from soft limits
journal, June 2016

Unifying relations for scattering amplitudes
journal, February 2018

One-loop scattering equations and amplitudes from forward limit
journal, November 2015

Review of AdS/CFT Integrability, Chapter V.2: Dual Superconformal Symmetry
journal, August 2011

Parity Invariance For String In Twistor Space
journal, January 2004

Scattering equations and Kawai-Lewellen-Tye orthogonality
journal, September 2014

New “gauge” theories in six dimensions
journal, January 1998

A relation between tree amplitudes of closed and open strings
journal, May 1986

M5-brane and D-brane scattering amplitudes
journal, December 2017

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

Symmetry for Flavor-Kinematics Duality from an Action
journal, March 2017

Loop Integrands for Scattering Amplitudes from the Riemann Sphere
journal, September 2015

Is the neutrino a goldstone particle?
journal, September 1973

Scattering equations, twistor-string formulas and double-soft limits in four dimensions
journal, July 2016

Gravity from Rational Curves in Twistor Space
journal, April 2013

Strongly coupled gravity and duality
journal, September 2000

One-loop amplitudes on the Riemann sphere
journal, March 2016

A duality for the S matrix
journal, March 2010

Spinor helicity and dual conformal symmetry in ten dimensions
journal, August 2011

Britto-Cachazo-Feng-Witten–Type Recurrent Relations for Tree Superamplitudes of $D = 11$ Supergravity
journal, January 2017

Tree-level S matrix of Yang-Mills theory
journal, July 2004

Unification of residues and Grassmannian dualities
journal, January 2011

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

New relations for gauge-theory amplitudes
journal, October 2008

Infrared Photons and Gravitons
journal, October 1965

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

Supertwistor space for 6D maximal super Yang-Mills
journal, April 2010

Ward Identity and Scattering Amplitudes for Nonlinear Sigma Models
journal, February 2018

$D = 6$ , $N = (2, 0)$ and $N = (4, 0)$ theories
journal, March 2018

The Grassmannian origin of dual superconformal invariance
journal, March 2010

Ambitwistor strings and the scattering equations
journal, July 2014

Interacting chiral gauge fields in six dimensions and Born-Infeld theory
journal, March 1997

Exact coefficients for higher dimensional operators with sixteen supersymmetries
journal, September 2015

Bootstrapping solutions of scattering equations
journal, February 2019

Bootstrapping solutions of scattering equations
journal, February 2019

Perturbiner methods for effective field theories and the double copy
journal, October 2018

Two-loop scattering amplitudes: double-forward limit and colour-kinematics duality
journal, December 2019

Constructing $$ \mathcal{N} $$ = 4 Coulomb branch superamplitudes
journal, August 2019

Unified formalism for 6D superamplitudes based on a symplectic Grassmannian
journal, August 2019

On polarized scattering equations for superamplitudes of 11D supergravity and ambitwistor superstring
journal, November 2019

Polarized Scattering Equations for 6D Superamplitudes
journal, March 2019