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

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2];  [3];  [4];  [3];  [5]
  1. Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada); California Inst. of Technology, Pasadena (United States)
  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)
+ Show Author Affiliations

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.

Research Organization:
California Inst. of Technology, Pasadena, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
Grant/Contract Number:
SC0011632
OSTI ID:
1501468
Journal Information:
Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 9 Vol. 2018; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (13)

Supersymmetric S-matrices from the worldsheet in 10 and 11d text January 2019
Efficient Calculation of Crossing Symmetric BCJ Tree Numerators text January 2020
Bootstrapping solutions of scattering equations journal February 2019
Constructing $$ \mathcal{N} $$ = 4 Coulomb branch superamplitudes journal August 2019
Unified formalism for 6D superamplitudes based on a symplectic Grassmannian journal August 2019
Perturbiner methods for effective field theories and the double copy journal October 2018
On polarized scattering equations for superamplitudes of 11D supergravity and ambitwistor superstring journal November 2019
Two-loop scattering amplitudes: double-forward limit and colour-kinematics duality journal December 2019
Polarized Scattering Equations for 6D Superamplitudes journal March 2019
Perturbiner Methods for Effective Field Theories and the Double Copy text January 2018
Constructing $\mathcal{N}=4$ Coulomb Branch Superamplitudes text January 2019
Unified Formalism for 6D Superamplitudes Based on a Symplectic Grassmannian text January 2019
On polarized scattering equations for superamplitudes of 11D supergravity and ambitwistor superstring text January 2019

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Related Subjects

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