Determine the critical fermion flavor in three-dimensional QED using nonlocal gauge

We determine the critical fermion flavor for dynamical chiral symmetry breaking in three-dimensional quantum electrodynamics using nonlocal gauge (gauge parameter depends on the momentum or coordinate). The coupled Dyson–Schwinger equations of the fermion and gauge boson propagators are considered in the vicinity of the critical point. Illustrated by using the transverse vertex proposed by Bashir et al., we show that: for a variety of the transverse vertex, the critical flavor is still 128/3π2, the same as using the bare vertex.