E7(7) invariant Lagrangian of d=4 N=8 supergravity

TL;DR

This paper constructs an E7(7) invariant Lagrangian for four-dimensional N=8 supergravity, demonstrating superinvariance, supersymmetry closure, and implications for quantization without relying on Lagrange multipliers.

Contribution

It introduces a new E7(7) invariant Lagrangian for N=8 supergravity that maintains superinvariance and explores its quantization implications.

Findings

Proved superinvariance and supersymmetry closure of the new action.

Constructed the conserved E7(7) Noether current.

Analyzed the implications for quantization of supergravity.

Abstract

We present an E7(7) invariant Lagrangian that leads to the equations of motion of d=4 N=8 supergravity without using Lagrange multipliers. The superinvariance of this new action and the closure of the supersymmetry algebra are proved explicitly for the terms that differ from the Cremmer--Julia formulation. Since the diffeomorphism symmetry is not realized in the standard way on the vector fields, we switch to the Hamiltonian formulation in order to prove the invariance of the E7(7) invariant action under general coordinate transformations. We also construct the conserved E7(7)-Noether current of maximal supergravity and we conclude with comments on the implications of this manifest off-shell E7(7)-symmetry for quantizing d=4 N=8 supergravity, in particular on the E7(7)-action on phase space.