The N=8 Supergravity Hamiltonian as a Quadratic Form

TL;DR

This paper proposes that the light-cone Hamiltonian of N=8 Supergravity can be written as a quadratic form, a property unique to maximally supersymmetric theories, and verifies this to second order.

Contribution

It introduces a quadratic form representation of the N=8 Supergravity Hamiltonian and demonstrates its validity up to second order in the coupling constant.

Findings

Hamiltonian expressed as a quadratic form

Verification of the quadratic form to second order

Uniqueness of this property to maximally supersymmetric theories

Abstract

We conjecture that the light-cone Hamiltonian of N=8 Supergravity can be expressed as a quadratic form. We explain why this rewriting is unique to maximally supersymmetric theories. The N=8 quartic interaction vertex is constructed and used to verify that this conjecture holds to second order in the coupling constant.