The O(N) model on a squashed S^3 and the Klebanov-Polyakov correspondence

TL;DR

This paper studies the large N O(N) vector model on a squashed three-sphere with a conformal mass, matching its strongly coupled behavior to bulk AdS geometries via the Klebanov-Polyakov correspondence, revealing consistent free energy behavior across parameters.

Contribution

It provides the first detailed match between the O(N) model on a squashed sphere and bulk AdS geometries, extending the AdS/CFT correspondence to non-trivial boundary geometries.

Findings

The field theory reproduces the bulk free energy's dependence on the squashing parameter.

The O(N) model remains in a symmetric phase for all finite couplings and squashing values.

The model's behavior persists even with negative boundary scalar curvature.

Abstract

We solve the O(N) vector model at large N on a squashed three-sphere with a conformal mass term. Using the Klebanov-Polyakov version of the AdS_4/CFT_3 correspondence we match various aspects of the strongly coupled theory with the physics of the bulk AdS Taub-NUT and AdS Taub-Bolt geometries. Remarkably, we find that the field theory reproduces the behaviour of the bulk free energy as a function of the squashing parameter. The O(N) model is realised in a symmetric phase for all finite values of the coupling and squashing parameter, including when the boundary scalar curvature is negative.