The O(N) model on a squashedS³and the Klebanov-Polyakov correspondence

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.

NUTs and bolts beyond Lovelock

“…One of the motivations for this work, and an obvious application of our results, can be found in the holographic context. There, Taub solutions with CP D−2 2 base spaces generically dominate the semiclassical partition function for holographic theories on a particularly interesting class of squashed spheres [60][61][62][63][64]. The fact that their thermodynamic properties can be computed analytically makes our solutions particularly appealing from a holographic perspective.…”

“…When 4f ∞ n 2 = L 2 , the previous metric is the one of a round S 3 . For any other value of n, it is the metric of a squashed sphere, and it is customary [60][61][62][63][64] to rewrite the NUT charge in terms of a 'squashing parameter' α as 4f ∞ n 2 /L 2 = 1/(1 + α). In order to specify the solution, we need to choose a boundary condition at some finite r = r b .…”

A study of quantum field theories in AdS at finite coupling

“…It is not clear that commuting these operations is always allowed. 32 One might be especially wary of commuting with the OPE expansion if the spectral representation is strictly-speaking not well-defined for the terms that are retained, as is the case for the power-law contribution of the identity, whose spectral representation can only be defined via an analytic continuation. 33 One step towards a more rigorous version of this argument would require to compute the spectral transform of a generic bulk block, 34 and study its large-ν behavior.…”

Partition functions on slightly squashed spheres and flux parameters

“…Their defining property is the following [64,69,70]. Consider a general static and spherically symmetric metric of the form 19) and let L N,V ≡ √ −gL| N,V be the effective Lagrangian resulting from the evaluation of L on (2.19). We say the corresponding theory is of the GQT class if the Euler-Lagrange equation of V associated to L V ≡ L N =1,V is identically satisfied.…”