p-Brane Dyons and Electric-magnetic Duality

TL;DR

This paper explores the properties of dyons and electric-magnetic duality in abelian p-form theories across different spacetime dimensions, revealing dimension-dependent quantization conditions and a symmetric two-potential formulation.

Contribution

It introduces a unified analysis of charge quantization and duality for self-interacting p-form theories, highlighting differences between odd and even p cases and providing a two-potential framework.

Findings

Quantization conditions differ for odd and even p.

Duality properties depend on the parity of p.

A two-potential formulation treats electric and magnetic sources symmetrically.

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.