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 T-pq which are coset spaces [SU(2)XSU(2)]/U(1). The central charge and a part of the chiral spectrum are calculated, respectively, from the volume of T-pq and the spectrum of the scalar Laplacian. Of the manifolds considered, only T-11 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 T-11 theory by supergravity: it is 27/32 of the central charge of the N = 2Z(2) orbifold theory from which it descends a renormalization group flow. [S0556-2821(98)03524-3].