Weyl Charges in Asymptotically Locally AdS$_3$ Spacetimes

TL;DR

This paper extends boundary conditions in 3D AdS gravity to include Weyl transformations, revealing a richer asymptotic symmetry algebra with non-trivial Weyl charges and an associated anomaly, advancing holographic understanding.

Contribution

It introduces an extended boundary condition framework in AdS$_3$ gravity that incorporates Weyl transformations, leading to new insights into the asymptotic symmetry algebra and Weyl anomalies.

Findings

Weyl charges are non-vanishing and integrable but not conserved.

The asymptotic symmetry algebra includes a Weyl abelian sector with a central extension.

A holographic Weyl current satisfying an anomalous Ward-Takahashi identity is constructed.

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.