Weyl charges in asymptotically locally AdS3 spacetimes

Abstract

We discuss an enhancement of the Brown-Henneaux boundary conditions in three-dimensional AdS general relativity to encompass Weyl transformations of the boundary metric. The resulting asymptotic symmetry algebra, after a field-dependent redefinition of the generators, is a direct sum of two copies of the Witt algebra and the Weyl Abelian sector. The charges associated with Weyl transformations are nonvanishing, integrable but not conserved due to a flux driven by the Weyl anomaly coefficient. The charge algebra admits an additional nontrivial central extension in the Weyl sector, related to the well-known Weyl anomaly. We then construct the holographic Weyl current and show that it satisfies an anomalous Ward-Takahashi identity of the boundary theory.