Topological electric charge

Abstract

By treating magnetic charge as a gauge symmetry through the introduction of a “magnetic” pseudo four-vector potential, we show that it is possible to construct a topological electric charge from a theory which originally contains gauge magnetic charge. This is an explicit realization of the Montonen-Olive conjecture that there should exist a dual theory to the usual 't Hooft-Polyakov monopole theory in which the roles of the gauge and topological charges are reversed. The physical distinction between 't Hooft-Polyakov monopoles and the dual theory with electric charge is that the strong and weak coupling regimes are reversed. Physically this leads to the mass of the electrically charged soliton being on the order of (1/137)M W as opposed to the much larger mass (on the order of 137M W) of the magnetically charged soliton. Thus even forM W in the TeV range such an electrically charged particle could be observed at some future accelerator.