Holonomies, anomalies and the Fefferman-Graham ambiguity in AdS(3) gravity

Using the Chern-Simons formulation of (2 + 1)-gravity, we derive, for the g eneral asymptotic metrics given by the Fefferman-Graham-Lee theorems, the e mergence of the Liouville mode associated to the boundary degrees of freedo m of (2 + 1)-dimensional anti-de-Sitter geometries. Holonomies are describe d through multi-valued gauge and Liouville fields and are found to algebrai cally couple the fields defined on the disconnected components of spatial i nfinity. Ln the case of flat boundary metrics, explicit expressions are obt ained for the fields and holonomies. We also show the link between the vari ation under diffeomorphisms of the Einstein theory of gravitation and the W eyl anomaly of the conformal theory at infinity, (C) 2001 Elsevier Science B.V. All rights reserved.