arXiv subjects
Publications and source records attributed to Jorge Conde.
We study the Goursat or characteristic problem, i.e. a hyperbolic equation with given data on a surface (the half of the standard Cauchy problem), with some kind of dimensional regularization procedure to deal with the divergences that appear. We will also comment some possible relation with a holographic setup.
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 $6\leq d\leq 10$ and some comments are made on its general structure and, in particular, on its relationship with the conformal anomaly, which we compute in dimension $d=8$.
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 cosmological constant.
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 $A_6\times C_4$ is proposed. The conjecture is that there is a Four-dimensional Euclidean Conformal Field Theory (ECFT) defined on a codimension two {\em submanifold} of the manifold $A_6$ (where one of the two remaining {\em 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, $c\sim l^4$.
This paper has been superseded by hep-th/0303164, "The Dirichlet Obstruction in AdS/CFT"
The low energy physics as predicted by strings can be expressed in two (conformally related) different variables, usually called {\em frames}. The problem is raised as to whether it is physically possible in some situations to tell one from the other.