Antisymmetric tensor fields on spheres: functional determinants and non--local counterterms

TL;DR

This paper computes the spectrum and functional determinants of the Hodge--de Rham Laplacian on spheres acting on antisymmetric tensor fields, deriving new non--local counterterms in the quantum effective action expressed via Betti numbers.

Contribution

It provides explicit spectrum expressions and evaluates functional determinants, introducing new non--local counterterms in quantum field theory on spheres.

Findings

Explicit spectrum expressions for antisymmetric tensor fields on spheres.

Evaluation of functional determinants and heat kernel expansion.

Derivation of new non--local counterterms related to Betti numbers.

Abstract

The Hodge--de Rham Laplacian on spheres acting on antisymmetric tensor fields is considered. Explicit expressions for the spectrum are derived in a quite direct way, confirming previous results. Associated functional determinants and the heat kernel expansion are evaluated. Using this method, new non--local counterterms in the quantum effective action are obtained, which can be expressed in terms of Betti numbers.