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 ≤ d ≤ 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.

An elementary introduction to Maldacena's AdS/CFT correspondence is given, with some emphasis in the Fefferman-Graham construction. This is based on lectures given by one of us (E.A.) at the Universidad Autonoma de Madrid.

A holographic interpretation for some specific Ricci flat string backgrounds of the form A 6 × C 4 is proposed. The conjecture is that there is a Four-dimensional Euclidean Conformal Field Theory (ECFT) defined on a codimension two submanifold of the manifold A 6 (where one of the two remaining holographic coordinates of A 6 is timelike, and the other one spacelike), with central charge proportional to the radius of curvature of the six-dimensional manifold, c ∼ l 4 .

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