AdS/CFT for non-boundary manifolds

Abstract

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 S1 ×S3 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.