Phase Space Renormalization and Finite BMS Charges in Six Dimensions

TL;DR

This paper analyzes the solution space of six-dimensional Einstein gravity, demonstrating the existence of infinite-dimensional asymptotic symmetries and their relation to soft-graviton theorems through a novel phase space renormalization technique.

Contribution

It introduces a new covariant phase space renormalization method and establishes the presence of infinite-dimensional BMS-like symmetries in six-dimensional gravity.

Findings

Infinite-dimensional supertranslation and superrotation symmetries in 6D gravity.

Non-integrability of the associated Hamiltonian charges.

Connection between Ward identities and soft-graviton theorems.

Abstract

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.