Weyl Charges in Asymptotically Locally AdS$_3$ Spacetimes

TL;DR

This work extends Brown–Henneaux boundary conditions in AdS$_3$ to include boundary Weyl rescalings, yielding an asymptotic symmetry algebra that is the direct sum of two Witt algebras plus a Weyl abelian sector. After a field-dependent redefinition, the charges split into conventional Virasoro-like components and a Weyl sector with a nontrivial central extension tied to the Weyl anomaly, making Weyl charges finite and integrable but not conserved due to boundary flux. The authors construct holographic Weyl currents and demonstrate an anomalous Ward–Takahashi identity on the boundary, linking bulk Weyl charges to boundary conformal anomaly. These results illuminate the role of Weyl transformations in the holographic dictionary for AdS$_3$ and suggest avenues for exploring Weyl sectors in higher dimensions and flat-hspace limits.

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 to Weyl transformations are non-vanishing, integrable but not conserved due to a flux driven by the Weyl anomaly coefficient. The charge algebra admits an additional non-trivial 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.