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

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.