Aspects of screening and confinement in a topologically massive $U{\left( 1 \right)_{\cal W}} \times U{(1)_{\cal Y}}$ Chern-Simons-Higgs theory

TL;DR

This paper investigates how a Chern-Simons mixing term affects confinement and screening in a 2+1 dimensional topologically massive Abelian gauge theory, revealing conditions for confinement or screening.

Contribution

It analyzes the impact of a Chern-Simons mixing term on physical observables in a topologically massive $U(1) imes U(1)$ theory, showing how it leads to confinement or screening depending on the effective model.

Findings

Interaction energy shows linear confinement in one effective model.

In another effective model, the phase is purely screening.

The Chern-Simons mixing term influences the confinement properties.

Abstract

By using the gauge-invariant but path-dependent, variables formalism, we consider a recently proposed topologically massive $U{\left( 1 \right)_{\cal W}} \times U{(1)_{\cal Y}}$ Chern-Simons-Higgs theory in $2+1$ dimensions. In particular, we inspect the impact of a Chern-Simons mixing term between two Abelian gauge fields on physical observables. We pursue our investigation by analysing the model in two different situations. In the first case, where we integrate out the massive excitation and consider an effective model for the massless field, we show that the interaction energy contains a linear term leading to the confinement of static charge probes along with a screening contribution. The second situation, where the massless field can be exactly integrated over with its constraint duly taken into account, the interesting feature is that the resulting effective model describes a purely screening phase, without any trace of a confining regime.