TL;DR
This paper calculates the effective action for scalar fields on orbifolded spheres using Barnes zeta-functions and provides numerical results, along with an analytical derivation related to symmetry planes of regular solids.
Contribution
It introduces a method to compute the effective action on orbifolded spheres using Barnes zeta-functions and derives a new analytical formula for symmetry planes of regular solids.
Findings
Effective action expressed via Barnes zeta-functions.
Numerical values for the effective action are provided.
An analytical derivation of the Cesàro-Fedorov formula is presented.
Abstract
The effective action on an orbifolded sphere is computed for minimally coupled scalar fields. The results are presented in terms of derivatives of Barnes zeta-functions and it is shown how these may be evaluated. Numerical values are shown. An analytical, heat-kernel derivation of the Ces\`aro-Fedorov formula for the number of symmetry planes of a regular solid is also presented.
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