AdS/CFT for non-boundary manifolds

In its Euclidean formulation, the AdS/CFT correspondence begins as a study ofYang-Mills conformal field theories on the sphere, S^4. It has beensuccessfully extended, however, to S^1 X S^3 and to the torus T^4. It isnatural to hope that it can be made to work for any manifold on which it ispossible to define a stable Yang-Mills conformal field theory. We consider apossible classification of such manifolds, and show how to deal with the mostobvious objection : the existence of manifolds which cannot be represented asboundaries. We confirm Witten's suggestion that this can be done with the helpof a brane in the bulk.Comment: 21 pages, 1 eps figure (1000x500), remarks on p-brane stress-tensor clarifie