Does the crossover from perturbative to nonperturbative physics in QCD become a phase transition at infinite N?

We present numerical evidence that, in the planar limit, four-dimensional Euclidean Yang-Mills theory undergoes a phase transition on a finite symmetrical four-torus when the length of the sides l decreases to a critical value l(c). For l > l(c) continuum reduction holds so that at leading order in N, there are no finite size effects in Wilson and Polyakov loops. This produces the exciting possibility of solving numerically for the meson sector of planar QCD at a cost substantially smaller than that of quenched SU(3). (C) 2003 Elsevier B.V. All rights reserved.