Confinement-Higgs Phase Crossover as a Lattice Artifact in 1+1 Dimensions

TL;DR

This paper investigates how lattice artifacts can induce a Higgs-like phase crossover in 1+1 dimensional massive Yang-Mills theory, which is normally confined with no Higgs phase in the continuum.

Contribution

It demonstrates that lattice regularization can produce a finite gluon mass and a Higgs-like crossover, contrasting the continuum theory's confined phase with no Higgs phase.

Findings

Lattice regularization yields a finite gluon mass in the model.

A smooth crossover to a Higgs phase can occur at finite volume and lattice spacing.

The Higgs phase observed matches lattice simulation results at N=2.

Abstract

We examine the phase structure of massive Yang-Mills theory in 1+1 dimensions. This theory is equivalent to a gauged principal chiral sigma model. It has been previously shown that the gauged theory has only a confined phase, and no Higgs phase in the continuum, and at infinite volume. There are no massive gluons, but only hadron-like bound states of sigma-model particles. The reason is that the gluon mass diverges, being proportional to the two-point correlation function of the renormalized field of the sigma model at $x=0$. We use exact large-$N$ results to show that after introducing a lattice regularization and typical values of the coupling constants used in Monte Carlo simulations, the gluon mass becomes finite, and even sometimes small. A smooth crossover into a Higgs phase can then appear. For small volumes and large $N$, we find an analytic expression for the gluon mass, which depends on the coupling constants and the volume. We argue that this Higgs phase is qualitatively similar to the one observed in lattice computations at $N=2$.