Comments on three-branes

The Born-Infeld-like effective world-volume theory of a single 3-brane is deduced from a manifestly space-time supersymmetric description of the corresponding D-brane. This is shown to be invariant under SL(2, R) transformations that act on the abelian gauge field as well as the bulk fields. The effective theory of two nearby parallel three-branes involves massive world-volume supermultiplets which transform under SL(2, Z) into the dyonic solitons of four-dimensional N = 4 spontaneously broken SU(2) Yang-Mills theory.