Dimensional reduction and the Yang-Mills vacuum state in2+1dimensions

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 Schr\"odinger 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 nonzero, and a nonzero 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.