E_7(7) on the Light Cone

TL;DR

This paper utilizes the E_7(7) symmetry of N=8 Supergravity to derive its light-cone Hamiltonian and transformations, revealing the structure of the theory at order  in the coupling constant.

Contribution

It provides the explicit form of the on-shell Hamiltonian and symmetry transformations of N=8 Supergravity in light-cone gauge, incorporating E_7(7) symmetry at order .

Findings

Derived the light-cone E_7(7) transformations of all fields.

Expressed the Hamiltonian as a quadratic form in the superfield.

Established the supersymmetry transformations to order .

Abstract

We use the Cremmer-Julia E_7(7) non-linear symmetry of N=8 Supergravity to derive its order $\kappa^2$ on-shell Hamiltonian in terms of one chiral light-cone superfield. By requiring that E_7(7) commute with the super-Poincare group, we deduce to lowest non-trivial order in $\kappa$, the light cone E_7(7) transformations of all fields of the theory, including the graviton. We then derive the dynamical supersymmetry transformation to order $\kappa^2$, and express the Hamiltonian as a quadratic form in the chiral superfield.