  We study N=1 gauge theories obtained by adding finite mass terms to N=4
Yang-Mills theory. The Maldacena dual is nonsingular: in each of the many
vacua, there is an extended brane source, arising from Myers' dielectric
effect. The source consists of one or more (p,q) 5-branes. In particular, the
confining vacuum contains an NS5-brane; the confining flux tube is a
fundamental string bound to the 5-brane. The system admits a simple
quantitative description as a perturbation of a state on the N=4 Coulomb
branch. Various nonperturbative phenomena, including flux tubes, baryon
vertices, domain walls, condensates and instantons, have new, quantitatively
precise, dual descriptions. We also briefly consider two QCD-like theories. Our
method extends to the nonsupersymmetric case. As expected, the N=4 matter
cannot be decoupled within the supergravity regime.
