Two-dimensional phase structure of SU(2) gauge-Higgs model

TL;DR

This study investigates the phase structure of the two-dimensional SU(2) gauge-Higgs model using lattice simulations, revealing a smooth crossover between confinement-like and Higgs-like regions without a true phase transition.

Contribution

First lattice simulation analysis of the 2D SU(2) gauge-Higgs model showing no phase transition, supporting the Fradkin-Shenker-Osterwalder-Seiler theorem.

Findings

Confinement-like and Higgs-like regions coexist in 2D.

Plaquette expectation value shows a smooth crossover.

Static potential exhibits string breaking and massive behavior.

Abstract

We study the phase structure of SU(2) gauge-Higgs model in two dimensions using lattice simulations. We show the result for the plaquette expectation value, static potential, and W propagator. Our results suggest that a confinement-like region and a Higgs-like region appear even in two dimensions. The behavior of the plaquette expectation value is consistent with a smooth cross-over in accordance with the Fradkin-Shenker-Osterwalder-Seiler theorem. In the confinement-like region, the static potential seems to rise linearly with string breaking at large distances, while in the Higgs-like region there seems to be a massive behavior which means that the BEH mechanism occurs. The correlation length obtained from the W propagator has a finite maximum between these phases, which supports no second-order phase transition. Based on these results, we suggest that there is no phase transition in two dimensions.