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

Abstract

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).

8p, 5 figures, revtex4

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• Large N Field Theories, String Theory and Gravity
• SU(N) gauge theories in four dimensions: exploring the approach to N = infinity
• Large N reduction in the continuum three dimensional Yang-Mills theory
• The deconfinement transition in SU(N) gauge theories
• A variant approach to the overlap action
• Proposal for the numerical solution of planar QCD
• The large-N phase transition of lattice SU(N) gauge theories

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