Abstract
We investigate the canonical formulation of the (bosonic) E6(6) exceptional field theory. The explicit non-integral (not manifestly gauge invariant) topological term of E6(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 E6(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.
Highlights
In 1978 it was discovered that toroidal compactifications of eleven-dimensional supergravity lead to emerging hidden global exceptional En(n)(R) symmetries in (11−n)-dimensional maximal supergravity [1, 2]
We investigate the canonical formulation of the E6(6) exceptional field theory
When acting with HDiff on the spatial vielbein (5.15) and the scalar fields (5.17) we find that the resulting gauge transformations are the covariantised versions of standard diffeomorphisms, where all derivatives are replaced by covariant derivatives
Summary
In 1978 it was discovered that toroidal compactifications of eleven-dimensional supergravity lead to emerging hidden global exceptional En(n)(R) symmetries in (11−n)-dimensional maximal supergravity [1, 2]. The existence of the exceptional symmetries in maximal supergravity theories continues to be one of their most remarkable features and remains to be fully understood at the quantum level It is only since 2013 that so-called “exceptional field theories” are known, which are fully and manifestly En(n)(R) covariant and which encompass eleven-dimensional supergravity [3]. See reference [4] for a recent review of exceptional field theories These exceptional field theories achieve (local) En(n)(R) covariance with the use of an extended generalised exceptional geometry and can be reduced to eleven-dimensional supergravity upon the solution of a consistency condition called the section condition. A central result in this work is the calculation of the canonical Hamiltonian of (bosonic) E6(6) exceptional field theory (1.1), written here on the primary constraint surface, with Π(X) indicating the canonical momenta conjugate to some fields X and PMm (A) being a modified version of the one-form momenta..
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