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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 formulasmore » for five-dimensional SYM and SUGRA amplitudes, as well as massive amplitudes of four-dimensional N = 4 SYM on the Coulomb branch.« less

Authors:
 [1];  [2];  [3];  [4];  [3];  [5]
  1. Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
  2. Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada); Univ. of Waterloo, Waterloo, ON (Canada); Univ. de Concepcion, Concepcion (Chile)
  3. California Inst. of Technology (CalTech), Pasadena, CA (United States)
  4. Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada); Univ. of Waterloo, Waterloo, ON (Canada)
  5. California Inst. of Technology (CalTech), Pasadena, CA (United States); Queen Mary Univ. of London, London (United Kingdom)
Publication Date:
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.
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.
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.
@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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