The String Dual of a Confining Four-Dimensional Gauge Theory

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.