Canonical analysis of E$_{6(6)}(\mathbb{R})$ invariant five dimensional (super-)gravity

TL;DR

This paper performs a detailed canonical analysis of five-dimensional supergravity with E$_{6(6)}$ invariance, deriving constraints, gauge transformations, and the Hamiltonian structure to understand its fundamental degrees of freedom.

Contribution

It provides the first complete Hamiltonian formulation of E$_{6(6)}$ invariant supergravity, including constraints, gauge algebra, and degrees of freedom.

Findings

Derived the full set of canonical constraints.

Determined the gauge transformation algebra.

Constructed the extended Hamiltonian for the theory.

Abstract

We investigate the canonical structure of the bosonic sector of the unique maximal supergravity theory in five dimensions that is manifestly invariant under the global action of E$_{6(6)}(\mathbb{R})$. Starting from the Lagrangian formulation of the theory we construct the Hamiltonian formulation and the full set of canonical constraints. We determine all gauge transformations and compute the algebra formed by the canonical constraints under the Poisson bracket. We re-derive the number of physical degrees of freedom and construct the extended Hamiltonian, describing the most general time evolution of the theory, where the full gauge freedom is manifest.