Large N reduction in the continuum three dimensional Yang-Mills theory

TL;DR

Three-dimensional Euclidean Yang-Mills theory in the planar limit undergoes a phase transition on a torus of side l=l(c) as expected of a noninteracting string theory and the situation in four dimensions is expected to be similar.

Abstract

Numerical and theoretical evidence leads us to propose the following: Three dimensional Euclidean Yang-Mills theory in the planar limit undergoes a phase transition on a torus of side $l=l_c$. For $l>l_c$ the planar limit is $l$-independent, as expected of a non-interacting string theory. We expect the situation in four dimensions to be similar.

Figures (2)

• Figure 1: Eigenvalue density distribution of a $4\times 4$ Wilson loop on $4^3$(folded) and $6^3$(unfolded) at $b=0.66$ and $N=23$.
• Figure 2: Eigenvalue density distribution of $L\times L$ Wilson loop on $L^3$ for $L/b=5$ and $L=4,6$. $N$ is set to $23$.