Forms on Vector Bundles Over Compact Real Hyperbolic Manifolds

TL;DR

This paper investigates gauge theories involving abelian p-forms on compact hyperbolic manifolds, analyzing spectral functions and tensor kernel trace formulas to understand their mathematical structure.

Contribution

It introduces a detailed spectral analysis of abelian p-form gauge fields on compact hyperbolic manifolds, linking trace formulas with spectral functions.

Findings

Derived explicit trace formulas for gauge fields

Analyzed spectral functions associated with these fields

Provided insights into the mathematical structure of gauge theories on hyperbolic manifolds

Abstract

We study gauge theories based on abelian $p-$ forms on real compact hyperbolic manifolds. The tensor kernel trace formula and the spectral functions associated with free generalized gauge fields are analyzed.