On condensation of charged scalars in D=3 dimensions

TL;DR

This paper investigates how condensates affect physical observables in a three-dimensional Higgs-like model, revealing screening or confinement phases depending on the mass term and Chern-Simons inclusion.

Contribution

It introduces a gauge-invariant, path-dependent formalism to analyze condensate effects and uncovers novel confinement and screening phenomena in three-dimensional gauge theories.

Findings

Physical mass term leads to screening potential.

Wrong-sign mass term results in confinement with linear potential.

Chern-Simons term induces an exact screening phase.

Abstract

By using the gauge-invariant, but path-dependent, variables formalism, we study the impact of condensates on physical observables for a three-dimensional Higgs-like model. As a result, for the case of a physical mass term like $m_H^2 \phi ^ * \phi$, we recover a screening potential. Interestingly enough, in the case of a "wrong-sign" mass term $- m_H^2 \phi ^ * \phi$, unexpected features are found. It is shown that the interaction energy is the sum of an effective-Bessel and a linear potential, leading to the confinement of static charges. However, when a Chern-Simons term is included, the surprising result is that the theory describes an exactly screening phase.