Dimensional Reduction and the Yang-Mills Vacuum State in 2+1 Dimensions

TL;DR

This paper introduces an approximation to the Yang-Mills vacuum state in 2+1 dimensions that satisfies the Schrödinger equation, incorporates a mass parameter, and aligns well with lattice results for the mass gap.

Contribution

It proposes a new approximation to the Yang-Mills vacuum state in 2+1 dimensions that satisfies the Schrödinger equation and matches lattice results for the mass gap.

Findings

The approximation satisfies the Schrödinger equation in key limits.

The mass gap from the approximation agrees within a few percent with lattice results.

Confinement is achieved through dimensional reduction with a non-zero mass parameter.

Abstract

We propose an approximation to the ground state of Yang-Mills theory, quantized in temporal gauge and 2+1 dimensions, which satisfies the Yang-Mills Schrodinger equation in both the free-field limit, and in a strong-field zero mode limit. Our proposal contains a single parameter with dimensions of mass; confinement via dimensional reduction is obtained if this parameter is non-zero, and a non-zero value appears to be energetically preferred. A method for numerical simulation of this vacuum state is developed. It is shown that if the mass parameter is fixed from the known string tension in 2+1 dimensions, the resulting mass gap deduced from the vacuum state agrees, to within a few percent, with known results for the mass gap obtained by standard lattice Monte Carlo methods.