Higher spins, quadratic forms and amplitudes

TL;DR

This paper demonstrates that light-cone higher spin theories, including supersymmetric cases, have Hamiltonians expressed as quadratic forms, linking scattering amplitudes to known gauge theory vertices.

Contribution

It extends the quadratic form structure of light-cone Hamiltonians from spin 1 and 2 to higher spins, revealing new connections to scattering amplitudes and supersymmetry.

Findings

Higher spin Hamiltonians are quadratic forms at first order in coupling.

Scattering amplitude structures naturally emerge from this framework.

The momentum space vertex relates to N=4 Yang-Mills theory.

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.