The whole idea of holography as put forward by Gerard 't Hooft assumes that data on a boundary determine physics in the volume. This corresponds to a Dirichlet problem for euclidean signature, or to a Goursat (characteristic) problem in the lorentzian setting. Is this last aspect of the problem that is explored here for Ricci flat spaces with vanishing… (More)
Some Ricci flat string backgrounds of the form M 6 × C 4 are introduced which admit a holographic interpretation in the following sense. There is a Four-dimensional Euclidean Conformal Field Theory (ECFT) defined on a codimension two boundary of the manifold M 6 (where one of the two remaining holographic coordinates of M 6 is timelike, and the other one… (More)
A new family of non critical bosonic string backgrounds in arbitrary space time dimension D and with ISO(1, D − 2) Poincaré invariance are presented. The metric warping factor and dilaton agree asymptotically with the linear dilaton background. The closed string tachyon equation of motion enjoys, in the linear approximation, an exact solution of " kink "… (More)
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.
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… (More)
AdS 5 with linear dilaton and non vanishing B-field is shown to be a solution of the non critical string beta function equations. A non critical (D = 5) solution interpolating between flat space-time and AdS 5 , with asymptotic linear dilaton and non vanishing B-field is also presented. This solution is free of space-time singularities and has got the… (More)
Sigma model (α ′) corrections to the confining string background are obtained. The main result is that the Poincaré invariant ansatz is maintained. Physical conditions for the dissapearance of the naked singularity are discussed.
The relationship between Bach's tensor and the four dimensional conformal anomaly is clarified, as well as its rôle as an obstruction for a perturbative reconstruction of the hologram (a Dirichlet problem). Some considerations on the obstruction in higher dimensions are included and, in particular, a candidate for the Fefferman-Graham obstruction in six… (More)