AdS/CFT for non-boundary manifolds

In its Euclidean formulation, the AdS/CFT correspondence begins as a study of Yang-Mills conformal field theories on the sphere, S4. It has been successfully extended, however, to S1xS3 and to the torus T4. It is natural to hope that it can be made to work for any manifold on which it is possible to define a stable Yang-Mills conformal field theory. We consider a possible classification of such manifolds, and show how to deal with the most obvious objection: the existence of manifolds which cannot be represented as boundaries. We confirm Witten's suggestion that this can be done with the help of a brane in the bulk. (author)