Symmetries of Diff-invariant theories

Abstract: In this talk, I will consider a universal group of symmetries that are associated to embedded surfaces in a classical spacetime. In the codimension-2 case, we refer to these surfaces as corners, and the symmetry as the extended corner symmetry. In the context of the Einstein-Hilbert theory, we show that the Noether charges supported by such a corner coincide precisely with the extended corner symmetry. The inclusion of the embedding map into the phase space of the theory allows for a calculation of the algebra of charges. We then show that within the covariant phase space formalism, there is a precise way of extending the phase space such that all charges are integrable and associated with Hamiltonian vector fields on field space. The algebra of charges is then consistently represented in terms of the Poisson brackets of this extended phase space theory. This resolves an old conundrum in gravity, separating the notion of non-integrability from non-conservation. Finally, we discuss some recent work employing the orbit method which relates corners to certain symplectic reductions. This gives an entirely group theoretical characterization of corners without reference to an underlying classical spacetime, and thus might be regarded as the building blocks of a quantum theory.

HEP - theorymathematical physics

Audience: researchers in the topic

Physics @ Boundaries Workshop