Topological Characterization of Higher Dimensional Charged Taub-NUT Instantons

TL;DR

This paper extends the topological analysis of dyonic fields and magnetic flux quantization from four-dimensional spacetimes to higher dimensions, specifically within Lovelock--Maxwell solutions, revealing discrete electric fluxes as topological excitations.

Contribution

It generalizes the topological characterization and flux quantization of dyonic fields to higher dimensions using inhomogeneous geometries in Lovelock--Maxwell theories.

Findings

Magnetic flux corresponds to a topological excitation.

Electric flux becomes discrete in higher-dimensional solutions.

Results apply broadly to theories with topological charges.

Abstract

Recently, we have shown that non-selfdual self-gravitating dyonic fields with magnetic mass generalize the Dirac monopole. The unique topological index, which characterizes the field, is a four dimensional analogue of the famous monopole configuration. An unexpected result of this analysis is that the electric parameter can only take certain discrete values as a consequence of applying the path integral approach to quantize the magnetic flux. Here, we show how this result can be generalized to higher dimensions, considering a special type of inhomogeneous geometries. Our results apply to a vast range of theories and situations in which topological charges are present. For concreteness, we focus here on Lovelock--Maxwell solutions and show that the magnetic flux corresponds to a topological excitation and the electric flux becomes discrete.