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

TL;DR

The paper provides numerical evidence that in the large-N limit, four-dimensional Euclidean Yang-Mills theory exhibits a phase transition on a finite four-torus as the size decreases, impacting the understanding of nonperturbative physics.

Contribution

It demonstrates a phase transition in planar Yang-Mills theory on a finite torus, suggesting a potential numerical approach to studying planar QCD at large N.

Findings

Phase transition occurs at a critical torus size $l_c$

Continuum reduction holds for $l > l_c$ with no finite size effects

Potential to numerically solve for meson sector of planar QCD efficiently

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).