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We perform a complete and systematic analysis of the solution space ofsix-dimensional Einstein gravity. We show that a particular subclass ofsolutions -- those that are analytic near $\mathcal{I}^+$ -- admit anon-trivial action of the generalised Bondi-Metzner-van der Burg-Sachs (GBMS)group which contains \emph{infinite-dimensional} supertranslations andsuperrotations. The latter consists of all smooth volume-preservingDiff$\times$Weyl transformations of the celestial $S^4$. Using the covariantphase space formalism and a new technique which we develop in this paper (phasespace renormalization), we are able to renormalize the symplectic potentialusing counterterms which are \emph{local} and \emph{covariant}. The Hamiltoniancharges corresponding to GBMS diffeomorphisms are non-integrable. We show thatthe integrable part of these charges faithfully represent the GBMS algebra andin doing so, settle a long-standing open question regarding the existence ofinfinite-dimensional asymptotic symmetries in higher even dimensionalnon-linear gravity. Finally, we show that the semi-classical Ward identitiesfor supertranslations and superrotations are precisely the leading andsubleading soft-graviton theorems respectively.

Phase Space Renormalization and Finite BMS Charges in Six Dimensions