Holography and CFT on generic manifolds

It is shown how the AdS/CFT correspondence extends to a more general situat ion in which the first theory is defined on (d + 1)-dimensional manifold (M ) over tilde defined as the filling in of a compact d-dimensional manifold M. The stability of the spectral correspondence mass/conformal-weight under such geometry changes is also proven. (C) 1999 Elsevier Science B.V. All r ights reserved.