The NUTs and Bolts of Squashed Holography

TL;DR

This paper compares the behavior of free O(N) models and gravitational solutions on squashed three-spheres, revealing similar thermodynamic and probabilistic properties relevant to holography and de Sitter space.

Contribution

It provides new solutions in general relativity with negative cosmological constant and analyzes their thermodynamics alongside the free O(N) model on squashed spheres, linking field theory and gravity.

Findings

Both systems show similar qualitative behavior across boundary geometries.

The partition function acts as a normalisable Hartle-Hawking wave function.

Probability peaks at the round three sphere with low boundary geometries.

Abstract

We evaluate the partition function of the free O(N) model on a two-parameter family of squashed three spheres. We also find new solutions of general relativity with negative cosmological constant and the same double squashed boundary geometry and analyse their thermodynamic properties. Remarkably, both systems exhibit a qualitatively similar behaviour over the entire configuration space of boundary geometries. Recent formulations of dS/CFT enable one to interpret the field theory partition function as a function of the two squashing parameters as the Hartle-Hawking wave function in a minisuperspace model of anisotropic deformations of de Sitter space. The resulting probability distribution is normalisable and globally peaked at the round three sphere, with a low amplitude of boundary geometries with negative scalar curvature.