Effective actions on the squashed three-sphere

TL;DR

This paper calculates the effective actions of scalar and spin-half fields on a squashed three-sphere, revealing their thermal properties and connections to holography, especially in the high-temperature limit.

Contribution

It provides explicit formulas for effective actions on a squashed three-sphere and explores their high-temperature behavior, linking geometric deformation to thermodynamic properties.

Findings

Effective actions depend on the squashing parameter.

High-temperature free energies resemble those on a two-sphere.

Spinor fields exhibit unusual thermal periodicities.

Abstract

The effective actions of a scalar and massless spin-half field are determined as functions of the deformation of a symmetrically squashed three-sphere. The extreme oblate case is particularly examined as pertinant to a high temperature statistical mechanical interpretation that may be relevant for the holographic principle. Interpreting the squashing parameter as a temperature, we find that the effective `free energies' on the three-sphere are mixtures of thermal two-sphere scalars and spinors which, in the case of the spinor on the three-sphere, have the `wrong' thermal periodicities. However the free energies do have the same leading high temperature forms as the standard free energies on the two-sphere. The next few terms in the high-temperature expansion are also explicitly calculated and briefly compared with the Taub-Bolt-AdS bulk result.