Lattice QCD-2+1

TL;DR

This paper analyzes a 2+1-dimensional SU(N) lattice gauge theory in axial gauge, demonstrating finite vacuum energy at second order in weak-coupling perturbation theory, with confinement and area law behavior.

Contribution

It shows that despite non-locality, the vacuum energy remains finite at second order, suggesting all-order finiteness, and confirms confinement and area law in this gauge.

Findings

Finite vacuum energy density at second order in perturbation theory.

Heavy quarks are confined and the spectrum is gapped.

Wilson loop exhibits area decay, indicating confinement.

Abstract

We consider a 2+1-dimensional SU(N) lattice gauge theory in an axial gauge with the link field U in the 1-direction set to one. The term in the Hamiltonian containing the square of the electric field in the 1-direction is non-local. Despite this non-locality, we show that weak-coupling perturbation theory in this term gives a finite vacuum-energy density to second order, and suggest that this property holds to all orders. Heavy quarks are confined, the spectrum is gapped, and the space-like Wilson loop has area decay.