Hidden symmetries of M-theory and its dynamical realization

Abstract:
We discuss the West's conjecture on E11 as a hidden symmetry of M-theory and the role of a dual to gravity field within the conjecture. As a dynamical realisation of the latter we consider the linearized version of the duality-symmetric gravity within the PST-like formulation and study properties of the model. We observe that retaining the locality of the approach constraints the index structure of the dual to graviton field. Remarkably, the constraint corresponds to that of required for closing the levels zero and one subalgebra of the very-extended Kac-Moody hidden symmetry algebra of gravity in D dimensions. The same constraint is also responsible for removing the antisymmetric part of the originally unconstrained vielbein, thus leading to the Fierz-Pauli-type linearized theory of a spin-2 field. The extension of the model to gravity with a cosmological constant and matter fields is also discussed.