Effect of gauge boson mass on chiral symmetry breaking in QED${}_3$

Abstract

In three-dimensional quantum electrodynamics (QED${}_3$) with 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 $\xi$ is smaller than a finite critical value ${\xi }_{cv}$ but is suppressed when $\xi >{\xi }_{cv}$. We further show that the critical value ${\xi }_{cv}$ 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 $\xi$, 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 $\xi$ is generated via instanton effect in a compact QED${}_3$ of massless fermions, our result shows that CSB coexists with instanton effect in a wide region of $\xi$, which can be used to study the confinement-deconfinement phase transition.

34 pagess, 2 figures

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