Squashed Holography with Scalar Condensates

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.

35 pages, version 2: presentation changed and comments added

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Cited by in corpus (8)

• Review of the No-Boundary Wave Function
• Universality of squashed-sphere partition functions
• Partition functions on slightly squashed spheres and flux parameters
• An Hamilton-Jacobi formulation of anisotropic inflation
• Boson-fermion duality in a gravitational background
• Spinors in Supersymmetric dS/CFT
• A correspondence between strings in the Hagedorn phase and asymptotically de Sitter space
• Holographic QFTs on S${}^2\times$S${}^2$, spontaneous symmetry breaking and Efimov saddle points