Dyonic p-branes from self-dual (p + 1)-branes

The “electromagnetic” Sl(2;Z) duality group in spacetime dimension D = 4k can be given a Kaluza-Klein interpretation in D = 4K + 2 as the modular group of a compactifying torus. We show how dyonic 2(k − 1)-branes in D = 4k can be interpreted as self-dual (2k − 1)-branes in D = 4k + 2 wound around the homology cycles of the torus. In particular, dyons of the D = 4 N = 4 heterotic string theory are interpreted as winding modes of a D = 6 self-dual string, while D = 8 dyonic membranes are interpreted as wound 3-branes of D = 10 IIB superstring theory. We also discuss the T-dual IIA interpretations of D = 8 dyonic membranes.