Symmetries and Charges in Weyl-Fefferman-Graham Gauge

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.