Forms on Vector Bundles Over Hyperbolic Manifolds and the Conformal Anomaly

TL;DR

This paper derives explicit formulas for the conformal anomaly of abelian p-forms on hyperbolic manifolds, providing exact and numerical results up to p=4 and dimension 10, using zeta-function regularization.

Contribution

It introduces a new explicit formula for the conformal anomaly of skew-symmetric tensor fields on hyperbolic manifolds, with detailed calculations for specific cases.

Findings

Explicit formula for conformal anomaly derived

Numerical values computed for p-forms up to p=4

Anomaly values obtained for spaces up to dimension 10

Abstract

We study gauge theories based on abelian $p-$forms on real compact hyperbolic manifolds. An explicit formula for the conformal anomaly corresponding to skew--symmetric tensor fields is obtained, by using zeta--function regularization and the trace tensor kernel formula. Explicit exact and numerical values of the anomaly for $p-$forms of order up to $p=4$ in spaces of dimension up to $n=10$ are then calculated.