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

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.Comment: 45 pages, references adde

Hamiltonian dynamics and Faddeev–Jackiw formulation of 3D gravity with a Barbero–Immirzi like parameter

Abstract A detailed Dirac and Faddeev–Jackiw formulation of Bonzom–Livine model describing gravity in three dimensions is performed. The full structure of the constraints, the gauge transformations and the generalized Faddeev–Jackiw brackets are found. In addition, we show that the Faddeev–Jackiw and Dirac brackets coincide