't Hooft tensors as Kalb-Ramond fields of generalised monopoles in all odd dimensions: d=3 and d=5

TL;DR

This paper extends the 't Hooft tensor construction to all odd dimensions, explicitly demonstrating how generalized monopoles in 3 and 5 dimensions relate to Kalb-Ramond fields and topological invariants.

Contribution

It generalizes the 't Hooft tensor framework to odd dimensions, connecting monopoles with Kalb-Ramond fields and topological charges in a unified manner.

Findings

Explicit construction of 't Hooft tensors in 3 and 5 dimensions

Identification of Kalb-Ramond fields as 't Hooft tensors in odd dimensions

Expression of magnetic charges as topological invariants

Abstract

The Kalb-Ramond monopole, as discussed by Nepomechie, is identical with the (singular) Dirac monopole in d=3 dimensions. The latter can be described by the (regular) 't Hooft-Polyakov monopole, via the 't Hooft tensor construction. This construction is extended to arbitrary odd dimensions by performing the d=5 case explicitly, exploiting the (regular) `monopoles' of generalised Georgi-Glashow models and identifying their 't Hooft tensors as the Kalb-Ramond fields. The relevant `magnetic charges' are expressed as topological invariants.