Canonical analysis of E6(6)(R) invariant five dimensional (super-)gravity

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 [Formula: see text]. 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.

The canonical formulation of E6(6) exceptional field theory

“…This theory can also be obtained by a reduction of eleven-dimensional supergravity on a six-torus, although this does not directly lead to the manifestly E 6(6) invariant form. The canonical formulation and analysis of this theory has been investigated in [14].…”

“…The bosonic theory does not fix the sign of this constant, only its modulus and therefore its sign is conventional [16]. 3 The coefficient of the topological term of ungauged five-dimensional maximal supergravity, as described in [14] -we can call the coefficient κ 5 -is related to the that of ExFT by κ 5 = 1 4 κ. This is due to the use of the ungauged abelian field strength in the writing of the topological term.…”

“…The smeared constraint allows us to avoid having to write derivatives of Dirac delta distributions (see e.g. references [14,45] for the use of smeared constraints). The smearing function Φ nM (x, Y ) can be thought of as a tensor of test functions which allows us to integrate the…”

“…This work may be seen as an extension of the comprehensive canonical analysis of the maximal ungauged E 6(6) invariant supergravity theory in [14].…”

“…We calculate most of the gauge transformations generated by the canonical constraints in section 5. In section 6 we calculate parts of the algebra of the canonical constraints and discuss some speculative results based on references [11,14,15]. In section 7 we discuss the USp (8) symmetry and how the results of the previous sections can be translated into the generalised vielbein formulation canonically.…”