Brane dynamics and N=1 supersymmetric gauge theory

We discuss some aspects of the relation between space-time properties of branes in string theory, and the gauge theory on their world-volume, for models invariant under four supercharges in three and four dimensions. We show that a simple set of rules governing brane dynamics reproduces many features of gauge theory. We study theories with U(N-c), SO(N-c) and Sp(N-c) gauge groups and matter in the fundamental and two-index tensor representations, and use the brane description to establish Seiberg's electric-magnetic duality for these models. (C) 1997 Elsevier Science B.V.