Abstract
We solve, using localization, for the large-N master field of superYang-Mills theory. From that we calculate expectation values of large Wilson loops and the free energy on the four-sphere. At weak coupling, these observables only receive nonperturbative contributions. The analytic solution holds for a finite range of the ’t Hooft coupling and terminates at the point of a large-N phase transition. We find evidence that as the coupling is further increased the theory undergoes an infinite sequence of similar transitions that accumulate at infinity.