Einstein manifolds and conformal field theories

TL;DR

This work investigates conformal field theories dual to AdS_5×M_5 backgrounds for Einstein manifolds M_5 in the T^{pq} family. It computes the central charges from the volume of M_5 and analyzes the scalar Laplacian spectrum to identify operator dimensions, with T^{11} yielding a supersymmetric, conifold-related case. Field-theory anomaly matching reproduces the holographic central-charge reduction through an RG flow, providing a nontrivial check of AdS/CFT for a nontrivial Sasaki–Einstein space. The results show a protected sector of chiral primaries with Δ = 3k/2 and reveal a rich spectrum of irrational dimensions for non-protected operators, illustrating the depth of holographic duality beyond simple orbifolds. The paper also discusses broader implications for gauge invariance in holographic setups and suggests avenues linking T^{11} to conifold singularities via singular compactifications.

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.