Effective actions on squashed lens spaces

TL;DR

This paper calculates the effective actions for scalars and spinors on squashed lens spaces, exploring their high-temperature behavior and thermodynamic implications, with relevance to holography and string theory.

Contribution

It provides explicit formulas for functional determinants on squashed lens spaces, including the high-temperature limit and thermodynamic interpretations, extending previous geometric analyses.

Findings

High-temperature behavior depends on the squashing parameter and group order m.

Final results are consistent for odd and even m despite different intermediate steps.

Thermodynamic interpretation for spinors exists only under specific conditions (twisted periodicity, even m).

Abstract

As a technical exercise with possible relevance to the holographic principle and string theory, the effective actions (functional determinants) for scalars and spinors on the squashed three-sphere identified under the action of a cyclic group, Z_m, are determined. Especially in the extreme oblate squashing limit, which has a thermodynamic interpretation, the high temperature behaviour is found as a function of m. Although the intermediate details for odd and even m are different, the final answers are the same. A thermodynamic interpretation for spinors is possible only for twisted periodicity conditions and m even.