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

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

2000-08-18

arxiv.org/abs/hep-th/0008147v2

Nucl.Phys. B594 (2001) 329-353

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 26 pages, 1 figure, modified version that will appear in Nucl. Phys. B

Scientific paper

10.1016/S0550-3213(00)00636-2

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.

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