D-brane dualities as canonical transformations

We show that the SL(2,R) duality symmetry of type IIB superstring theory can be formulated as the canonical transformation interchanging momenta and magnetic degrees of freedom associated to the abelian world-volume gauge field of the D-3-brane. D-strings are shown to be connected under the corresponding transformation in the world-sheet to the (m, n) family of string solutions of type IIB supergravity constructed by Schwarz. For the type IIA superstring the D-2-brane is mapped under the three-dimensional world-volume electric-magnetic duality to the dimensional reduction of the membrane of M-theory.