Continuum Strong Coupling Expansion of Yang-Mills Theory: Quark Confinement and Infra-Red Slavery

TL;DR

This paper develops a continuum strong coupling expansion for four-dimensional Yang-Mills theory, demonstrating confinement and area law behavior at leading order by relating it to two-dimensional Yang-Mills theory.

Contribution

It introduces a novel expansion method in inverse coupling for Yang-Mills theory, linking it to solvable two-dimensional models to analyze confinement.

Findings

Wilson loop obeys an area law at leading order

Coupling becomes infinite as mass-scale approaches zero

Ground-state expectation values reduce to 2D Yang-Mills calculations

Abstract

We solve Schr\"odinger's equation for the ground-state of {\it four}-dimensional Yang-Mills theory as an expansion in inverse powers of the coupling. Expectation values computed with the leading order approximation are reduced to a calculation in {\it two}-dimensional Yang-Mills theory which is known to confine. Consequently the Wilson loop in the four-dimensional theory obeys an area law to leading order and the coupling becomes infinite as the mass-scale goes to zero.