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

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The `electromagnetic' Sl(2;) 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.