Squashed Holography with Scalar Condensates

Understand

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.