Effect of gauge boson mass on chiral symmetry breaking in three-dimensional QED

Abstract

In three-dimensional quantum electrodynamics $({\mathrm{QED}}_{3})$ with a massive gauge boson, we investigate the Dyson-Schwinger equation for the fermion self-energy in the Landau gauge and find that chiral symmetry breaking (CSB) occurs when the gauge boson mass $\ensuremath{\xi}$ is smaller than a finite critical value ${\ensuremath{\xi}}_{\mathrm{cv}}$ but is suppressed when $\ensuremath{\xi}>{\ensuremath{\xi}}_{\mathrm{cv}}.$ We further show that the critical value ${\ensuremath{\xi}}_{\mathrm{cv}}$ does not qualitatively change after considering higher order corrections from the wave function renormalization and vertex function. Based on the relation between CSB and the gauge boson mass $\ensuremath{\xi},$ we give a field theoretical description of the competing antiferromagnetic and superconducting orders and, in particular, the coexistence of these two orders in high temperature superconductors. When the gauge boson mass $\ensuremath{\xi}$ is generated via the instanton effect in a compact ${\mathrm{QED}}_{3}$ of massless fermions, our result shows that CSB coexists with the instanton effect in a wide region of $\ensuremath{\xi},$ which can be used to study the confinement-deconfinement phase transition.