Einstein Manifolds and Conformal Field Theories

In light of the AdS/CFT 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 fivedimensional manifolds T pq 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 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 in [1]. 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 = 2 Z2 orbifold theory from which it descends via an RG flow.