2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/197067We 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).8p, 5 figures, revtex4High Energy Physics - LatticeHigh Energy Physics - PhenomenologyHigh Energy Physics - Theorytext