Higher spins, quadratic forms and amplitudes

Abstract

The light-cone Hamiltonians for spin 1 and spin 2 fields, describing both the pure and the maximally supersymmetric theories, may be expressed as quadratic forms. In this paper, we show that this feature extends to light-cone higher spin theories. To first order in the coupling constant, we prove that the higher spin Hamiltonians, with and without supersymmetry, are quadratic forms. Scattering amplitude structures emerge naturally in this framework and we relate the momentum space vertex in a supersymmetric higher spin theory to the corresponding vertex in the N=4 Yang-Mills theory.

14 pages

References in corpus (22)

• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Cubic interaction vertices for massive and massless higher spin fields
• Cubic interaction vertices for fermionic and bosonic arbitrary spin fields
• Spacelike Singularities and Hidden Symmetries of Gravity
• KLT relations from the Einstein-Hilbert Lagrangian
• Non-linear Realization of PSU(2,2|4) on the Light-Cone
• The N=8 Supergravity Hamiltonian as a Quadratic Form
• Spinor helicity structures in higher spin theories
• Supersymmetric Yang-Mills Theories: not quite the usual perspective
• A manifestly MHV Lagrangian for N=4 Yang-Mills
• Yang-Mills theories and quadratic forms
• Gravity and Yang-Mills theory
• Exceptional versus superPoincaré algebra as the defining symmetry of maximal supergravity
• Factorization of cubic vertices involving three different higher spin fields
• E${}_8$ in $\mathcal{N}=8$ supergravity in four dimensions
• Gravitation and quadratic forms
• The BLG Theory in Light-Cone Superspace
• Deriving spin-1 quartic interaction vertices from closure of the Poincaré algebra
• Cubic interaction vertices in higher spin theories
• A hidden symmetry in quantum gravity
• Fermi-Bose cubic couplings in light-cone field theories

Cited by in corpus (6)

• Perturbative linearization of super-Yang-Mills theories in general gauges
• BMS algebra from residual gauge invariance in light-cone gravity
• Perturbative linearization of supersymmetric Yang-Mills theory
• Residual gauge symmetry in light-cone electromagnetism
• Supersymmetric Yang-Mills theory in D=6 without anti-commuting variables
• Nicolai maps and uniqueness in the light-cone gauge