Einstein manifolds and conformal field theories

TL;DR

This paper explores the relationship between Einstein manifolds and conformal field theories within the AdS/CFT framework, calculating central charges and spectra for specific manifolds, notably T^{11}, and matching supergravity predictions with field theory results.

Contribution

It provides explicit calculations of central charges and spectra for T^{pq} manifolds, identifying T^{11} as the unique supersymmetric case and confirming supergravity predictions through field theory analysis.

Findings

T^{11} admits supersymmetry and characterizes a supergravity solution.

The central charge for T^{11} matches supergravity predictions, being 27/32 of the Z_2 orbifold.

Spectrum calculations support the AdS/CFT correspondence for these manifolds.

Abstract

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 five-dimensional manifolds T^{pq} which are coset spaces (SU(2) x 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 hep-th/9807080. 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 Z_2 orbifold theory from which it descends via an RG flow.