Symmetries and Charges in Weyl-Fefferman-Graham Gauge

TL;DR

This paper explores the asymptotic symmetries of 3D AdS gravity in a generalized gauge that includes a Weyl connection, revealing new charged diffeomorphisms and implications for holographic renormalization.

Contribution

It introduces the Weyl-Fefferman-Graham gauge as a natural extension of the usual gauge, analyzing its symmetry structure and physical charges in the context of holography.

Findings

Charged diffeomorphisms in the Weyl-Fefferman-Graham gauge.

New insights into holographic renormalization in this gauge.

Physical implications of gauge transformations in boundary structures.

Abstract

We investigate the asymptotic symmetries of three-dimensional AdS Einstein gravity in the Weyl-Fefferman-Graham gauge, which is a generalization of the Fefferman-Graham gauge inducing a Weyl connection as part of the boundary structure. We show that this gauge arises as a natural intermediary step of the gauge-fixing procedure in the Chern-Simons formulation. We prove that the diffeomorphism required to go to the usual Fefferman-Graham gauge can be charged, and thus its implementation has physical repercussions. We discuss the holographic renormalization and the variational principle offering a new holographic take on this gauge and its charges.