The Dirichlet Obstruction in AdS/CFT

Abstract

The obstruction for a perturbative reconstruction of the five-dimensional bulk metric starting from the four-dimensional metric at the boundary,that is, the Dirichlet problem, is computed in dimensions $6\le d\le 10$ and some comments are made on its general structure and, in particular, on its relationship with the conformal anomaly, which we compute in dimension $d=8$.

13 pages, references added (this paper supersedes hep-th/0206140, "A Note on the Bach Tensor in AdS/CFT", which has been withdrawn)

References in corpus (1)

• Codimension Two Holography

Cited by in corpus (7)

• A classification of local Weyl invariants in D=8
• The tetralogy of Birkhoff theorems
• Conformal coupling of the scalar field with gravity in higher dimensions and invariant powers of the Laplacian
• Conformal invariant powers of the Laplacian, Fefferman-Graham ambient metric and Ricci gauging
• Higher Spin Interacting Quantum Field Theory and Higher Order Conformal Invariant Lagrangians
• Mass spectra of bottom-charm baryons
• Examining Instabilities Due to Driven Scalars in AdS