Noncompact three-dimensional quantum electrodynamics with Nf=1 and Nf=4

Abstract

We present numerical results for noncompact three-dimensional quantum electrodynamics for numbers of flavors ${N}_{f}=1$ and ${N}_{f}=4$. In particular, we address the issue of whether chiral symmetry is spontaneously broken in the continuum limit, and obtain a positive answer for ${N}_{f}=1$, with a dimensionless condensate estimated to be ${\ensuremath{\beta}}^{2}⟨\overline{\ensuremath{\psi}}\ensuremath{\psi}⟩\ensuremath{\simeq}O({10}^{\ensuremath{-}3})$, implying that the critical number of flavors ${N}_{fc}>1$. We also compare the ${N}_{f}=1$ and ${N}_{f}=4$ models by analyzing the transition from strong to weak coupling behavior using an equation of state based on a continuous phase transition. While some qualitative differences emerge, it appears difficult to determine whether ${N}_{f}=4$ lies above or below ${N}_{fc}$.