Phase space renormalization and finite BMS charges in six dimensions
Federico Capone, Prahar Mitra, Aaron Poole, Bilyana Tomova
Abstract
A bstract 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 $$ \mathcal{I} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>I</mml:mi> </mml:math> + — admit a non-trivial action of the generalised Bondi-Metzner-van der Burg-Sachs (GBMS) group which contains infinite-dimensional supertranslations and superrotations. The latter consists of all smooth volume-preserving Diff×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 local and 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.