Effective actions on the squashed 3-sphere

The effective actions of massless scalar and spin-½ fields are determined as functions of the deformation of a symmetrically squashed 3-sphere. The extreme oblate case is particularly examined as pertinent 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 3-sphere are mixtures of thermal 2-sphere scalars and spinors which, in the case of the spinor on the 3-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 2-sphere. The next few terms in the high-temperature series are also evaluated and briefly compared with the Taub-Bolt-AdS bulk result.