The canonical formulation of E$_{6(6)}$ exceptional field theory

TL;DR

This paper develops the canonical formulation of E$_{6(6)}$ exceptional field theory, including the topological term, canonical momenta, Hamiltonian, and gauge transformations, advancing understanding of its Hamiltonian structure.

Contribution

It provides the first detailed canonical formulation of E$_{6(6)}$ exceptional field theory, including the topological term and gauge structure, and explores its relation to generalized variables.

Findings

Constructed the topological term and canonical momenta.

Derived the canonical Hamiltonian and gauge transformations.

Discussed potential generalized Ashtekar variables.

Abstract

We investigate the canonical formulation of the (bosonic) E$_{6(6)}$ exceptional field theory. The explicit non-integral (not manifestly gauge invariant) topological term of E$_{6(6)}$ exceptional field theory is constructed and we consider the canonical formulation of a model theory based on the topological two-form kinetic term. Furthermore we construct the canonical momenta and the canonical Hamiltonian of the full bosonic E$_{6(6)}$ exceptional field theory. Most of the canonical gauge transformations and some parts of the canonical constraint algebra are calculated. Moreover we discuss how to translate the results canonically into the generalised vielbein formulation. We comment on the possible existence of generalised Ashtekar variables.