Squashed Holography with Scalar Condensates

TL;DR

This paper explores the holographic duality between scalar-deformed O(N) models on squashed spheres and Einstein gravity solutions in AdS/dS, revealing insights into thermodynamics, no-boundary measures, and anisotropic inflation.

Contribution

It provides a detailed analysis of scalar deformations in holographic models on squashed spheres and connects these to regular gravity solutions in AdS and dS, offering a new toy model for the no-boundary measure.

Findings

AdS solutions' thermodynamics match free O(N) model predictions.

dS solutions define a no-boundary measure over anisotropies.

Partition function yields a peaked probability distribution favoring round spheres.

Abstract

We evaluate the partition function of the free and interacting O(N) vector model on a two-parameter family of squashed three spheres in the presence of a scalar deformation. We also find everywhere regular solutions of Einstein gravity coupled to a scalar field in AdS and in dS with the same double squashed boundary geometry. Remarkably, the thermodynamic properties of the AdS solutions qualitatively agree with the behavior predicted by the free O(N) model with a real mass deformation. The dS bulk solutions specify the semiclassical `no-boundary' measure over anisotropic deformations of inflationary, asymptotic de Sitter space. Through dS/CFT the partition function of the interacting O(N) model yields a holographic toy model of the no-boundary measure. We find this yields a qualitatively similar probability distribution which is normalizable and globally peaked at the round three sphere, with a low amplitude for strong anisotropies.