Einstein manifolds and conformal field theories

In light of the anti--de Sitter space conformal field theory correspondence, it is natural to try to define a conformal field theory in a large N, strong coupling limit via a supergravity compactification on the product of an Einstein manifold and anti--de Sitter space. We consider the five-dimensional manifolds Tpq which are coset spaces [SU(2)×SU(2)]/U(1). The central charge and a part of the chiral spectrum are calculated, respectively, from the volume of Tpq and the spectrum of the scalar Laplacian. Of the manifolds considered, only T¹¹ admits any supersymmetry: it is this manifold which characterizes the supergravity solution corresponding to a large number of $D3$-branes at a conifold singularity, discussed recently by Klebanov and Witten. Through a field theory analysis of anomalous three point functions we are able to reproduce the central charge predicted for the T¹¹ theory by supergravity: it is 27/32 of the central charge of the N=2Z₂ orbifold theory from which it descends via a renormalization group flow.