E_7(7) on the Light Cone

TL;DR

This paper derives the order-$\kappa^2$ on-shell Hamiltonian of ${\cal N}=8$ Supergravity on the light cone by exploiting the non-linear $E_{7(7)}$ duality, expressing the result in terms of a single chiral light-cone superfield. By enforcing commutativity with the super-Poincaré algebra, the authors fix the light-cone $E_{7(7)}$ transformations for all fields, including the graviton, and obtain the dynamical supersymmetry variations to $\kappa^2$, enabling the Hamiltonian to be written as a quadratic form in the superfield. The analysis uses the $LC_2$ gauge to derive explicit vector and scalar Hamiltonians, then embeds everything in light-cone superspace where 256 physical degrees of freedom reside in one constrained chiral superfield, and delicately combines $E_{7(7)}$ with the ${\cal N}=8$ super-Poincaré algebra to yield compact all-order insights. The results suggest a remarkably simple all-orders structure for the non-linear $E_{7(7)}/SU(8)$ transformations and point toward broader applicability in higher-dimensional theories. Overall, the work provides a precise, symmetry-driven construction of the light-cone Hamiltonian and dynamical supersymmetry for ${\cal N}=8$ SUGRA and highlights the potential for further all-orders formulations.

Abstract

We use the Cremmer-Julia E_7(7) non-linear symmetry of N=8 Supergravity to derive its order $κ^2$ 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 $κ$, 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 $κ^2$, and express the Hamiltonian as a quadratic form in the chiral superfield.