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

TL;DR

This paper investigates the phase transition in three-dimensional Euclidean Yang-Mills theory in the planar limit, showing that for large enough torus size, the theory becomes independent of the size, indicating a non-interacting string phase.

Contribution

It provides numerical and theoretical evidence for a phase transition in 3D Yang-Mills theory at a critical torus size, suggesting a string-like behavior in the large N limit.

Findings

Identifies a critical size l_c where the phase transition occurs.

Shows the theory becomes size-independent for l > l_c.

Suggests similar behavior may occur in four dimensions.

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.