p-Brane Dyons and Electric-magnetic Duality

Abstract

We discuss dyons, charge quantization and electric-magnetic duality for self-interacting, abelian, p-form theories in the spacetime dimensions D=2(p+1) where dyons can be present. The corresponding quantization conditions and duality properties are strikingly different depending on whether p is odd or even. If p is odd one has the familiar eg'-ge'= 2nh, whereas for even p one finds the opposite relative sign, eg'+ge'= 2nh. These conditions are obtained by introducing Dirac strings and taking due account of the multiple connectedness of the configuration space of the strings and the dyons. A two-potential formulation of the theory that treats the electric and magnetic sources on the same footing is also given. Our results hold for arbitrary gauge invariant self-interaction of the fields and are valid irrespective of their duality properties.

Figures (1)

• Figure 1: Double pass. The string of dyon 1 goes towards dyon 2 without touching it, whereas that of dyon 2 goes towards dyon 1 again without touching it. The strings themselves do not touch either. Rather, string 1 is behind (more into the page than string 2). We now imagine a simultaneous full turn of both strings going out of the page in the $(x^1,x^2)$ plane orthogonal to the $x^3$ axis. The dyons are kept fixed. This "motion" describes a path in the configuration space of the dyons and the strings which we call "the double pass". The fact that string 1 does not touch dyon 2, and vice versa, is mandatory (Dirac veto). However, in the double pass we also require the strings not to touch each other at any "instant" during the motion that generates it. This is not mandatory in general, but it is what makes the double pass contractible to a point.