We perform a complete and systematic analysis of the solution space of six-dimensional Einstein gravity. We show that a particular subclass of solutions -- those that are analytic near $\mathcal{ I}^+$ -- admit a non-trivial action of the generalised Bondi-Metzner-van der Burg-Sachs (GBMS) group which contains \emph{ infinite-dimensional} supertranslations and superrotations. The latter consists of all smooth volume-preserving Diff$\times$Weyl transformations of the celestial $S^4$. Using the covariant phase space formalism and a new technique which we develop in this paper (phase space renormalization), we are able to renormalize the symplectic potential using counterterms which are \emph{ local} and \emph{ covariant}. The Hamiltonian charges corresponding to GBMS diffeomorphisms are non-integrable. We show that the integrable part of these charges faithfully represent the GBMS algebra and in doing so, settle a long-standing open question regarding the existence of infinite-dimensional asymptotic symmetries in higher even dimensional non-linear gravity. Finally, we show that the semi-classical Ward identities for supertranslations and superrotations are precisely the leading and subleading soft-graviton theorems respectively.
Categories: hep-th gr-qc