Topological Quantum Numbers of Dyonic Fields Over Taub-NUT and Taub-Bolt Spaces

Abstract

We calculate the Chern numbers of ${\rm SU}(2)$-homogeneous Einstein-Maxwell gravitational instantons with boundary at infinity. By restating these numbers as Chern-Simons invariants on the boundary apparent conflicting results emerge. We resolve this issue examining the topological stability of the self-gravitating Abelian fields. No quantization carrying physical meaning is found when the background is a Taub-NUT space. However the magnetic charge of dyons on Taub-Bolt spaces is found to be of topological quantum nature. In this framework electric charge is quantized by a consistency condition.