Holonomies, anomalies and the Fefferman-Graham ambiguity in AdS3 gravity

TL;DR

This paper explores the boundary degrees of freedom in (2+1)D AdS gravity using Chern-Simons theory, revealing how holonomies and anomalies relate to the Fefferman-Graham ambiguity and boundary Liouville modes.

Contribution

It derives the emergence of Liouville modes from asymptotic AdS metrics and describes how holonomies couple boundary fields, linking diffeomorphism variations to Weyl anomalies.

Findings

Holonomies couple boundary fields across disconnected components.

Explicit expressions for fields and holonomies in flat boundary cases.

Connection between diffeomorphism variations and Weyl anomalies.

Abstract

Using the Chern-Simon formulation of (2+1) gravity, we derive, for the general asymptotic metrics given by the Fefferman-Graham-Lee theorems, the emergence of the Liouville mode associated to the boundary degrees of freedom of (2+1) dimensional anti de Sitter geometries. Holonomies are described through multi-valued gauge and Liouville fields and are found to algebraically couple the fields defined on the disconnected components of spatial infinity. In the case of flat boundary metrics, explicit expressions are obtained for the fields and holonomies. We also show the link between the variation under diffeomorphisms of the Einstein theory of gravitation and the Weyl anomaly of the conformal theory at infinity.