p-Brane dyons and electric-magnetic duality

We discuss dyons, charge quantization and electric-magnetic duality for self-interacting, abelian, p-form theories in the space-time 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 eḡ − gē = 2φ, whereas for even p one finds the opposite relative sign, eḡ + gē = 2π. 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