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

TL;DR

This paper explores the interpretation of dyonic p-branes in certain dimensions as self-dual branes in higher dimensions, revealing a geometric understanding of duality symmetries through torus compactification.

Contribution

It provides a novel interpretation of dyonic branes as self-dual branes wound around a torus, linking duality groups to geometric properties of compactification.

Findings

Dyonic 2(k-1)-branes in D=4k are self-dual (2k-1)-branes in D=4k+2.

D=4 N=4 heterotic string dyons are winding modes of a D=6 self-dual string.

D=8 dyonic membranes correspond to wound 3-branes in D=10 IIB superstring.

Abstract

The `electromagnetic' $Sl(2;\bZ)$ 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.