Generalized Fefferman-Graham gauge and boundary Weyl structures

TL;DR

This paper extends the Fefferman-Graham gauge in AdS/CFT to include boundary Weyl structures, introduces new counterterms for holographic renormalization, and applies these to black hole and integrable models.

Contribution

It generalizes the FG gauge to restore boundary Weyl invariance and develops a Weyl covariant holographic renormalization scheme with new counterterms.

Findings

Weyl covariant holographic stress tensor derived

New corner counterterm ensures finiteness of action

Weyl anomaly expressed in a covariant form

Abstract

In the framework of AdS/CFT correspondence, the Fefferman--Graham (FG) gauge offers a useful way to express asymptotically anti-de Sitter spaces, allowing a clear identification of their boundary structure. A known feature of this approach is that choosing a particular conformal representative for the boundary metric breaks explicitly the boundary scaling symmetry. Recent developments have shown that it is possible to generalize the FG gauge to restore boundary Weyl invariance by adopting the Weyl--Fefferman--Graham gauge. In this paper, we focus on three-dimensional gravity and study the emergence of a boundary Weyl structure when considering the most general AdS boundary conditions introduced by Grumiller and Riegler. We extend the holographic renormalization scheme to incorporate Weyl covariant quantities, identifying new subleading divergences appearing at the boundary. To address these, we introduce a new codimension-two counterterm, or corner term, that ensures the finiteness of the gravitational action. From here, we construct the quantum-generating functional, the holographic stress tensor, and compute the corresponding Weyl anomaly, showing that the latter is now expressed in a full Weyl covariant way. Finally, we discuss explicit applications to holographic integrable models and accelerating black holes. For the latter, we show that the new corner term plays a crucial role in the computation of the Euclidean on-shell action.