Confinement of matter fields in compact (2+1)-dimensional QED theory of high-$T_{c}$ superconductors

TL;DR

This paper investigates how matter fields are confined in a compact (2+1)-dimensional QED model relevant to high-temperature superconductors, revealing conditions for confinement and symmetry breaking.

Contribution

It demonstrates that monopole configurations do not influence the gauge potential propagator, clarifying confinement mechanisms in different superconducting states.

Findings

Monopoles do not affect the gauge propagator.

Chiral symmetry breaking and confinement occur together in the antiferromagnetic state.

Monopoles and Anderson-Higgs do not induce confinement in the d-wave superconducting state.

Abstract

We study confinement of matter fields in the effective compact (2+1)-dimensional QED theory of high-$T_{c}$ superconductors. It is shown that the monopole configurations do not affect the propagator of gauge potential $a_{\mu}$. Based on this result, we found that: chiral symmetry breaking and confinement take place simultaneously in the antiferromagnetic state; neither monopole effect nor Anderson-Higgs mechanism can cause confinement in the d-wave superconducting state.