nLab Fefferman-Graham ambient construction

Idea

A construction in conformal geometry by which a conformal manifold is realized by embedding into a suitable ambient Einstein manifold.

Application in AdS-CFT

For application in the AdS-CFT correspondence see for instance (deHaro-Skenderis-Solodukhin 00, Tetradis 11).

Related concepts

• conformal compactification

• tractor bundle

References

General

• Charles Fefferman, Robin Graham, Conformal invariants, Asterisque: 95–116.

• Charles Fefferman, Robin Graham, The Ambient Metric, Princeton University Press., (2011)

• Wikipedia, Ambient construction

Application in AdS-CFT correspondence

References using the ambient construction in the context of the AdS-CFT correspondence include

• Sebastian de Haro, Kostas Skenderis, Sergey Solodukhin, Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence, Commun.Math.Phys. 217 (2001) 595-622 (arXiv:hep-th/0002230)

• N. Tetradis, Holographic Horizons (arXiv:1109.2335)