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

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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 formulasmore »« 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)

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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