Addendum to "Critical behaviour of ($2+1$)-dimensional QED: $1/N_f$-corrections in an arbitrary non-local gauge"

Abstract

Dynamical chiral symmetry breaking (D$\chi$SB) is studied within ($2+1$)-dimensional QED with $N$ four-component fermions. The leading and next-to-leading orders of the $N$ expansion were computed exactly in Refs.~[\onlinecite{Gusynin:2016som,Kotikov:2016prf}] in an arbitrary non-local gauge. In this addendum to [\onlinecite{Kotikov:2016prf}], we show that the resummation of the wave-function renormalization constant at the level of the gap equation yields a {\it complete} cancellation of the gauge dependence of the critical fermion flavour number resulting in: $N_c=2.8469$, which is such that D$\chi$SB takes place for $N<N_c$. The result is in full agreement with one of Ref.~[\onlinecite{Gusynin:2016som}].

(v2) 3+epsilon pages, published in PRD, 2 references added, no change in results (v1) 3 pages, no figure. addendum to arXiv:1609.06912

References in corpus (3)

• Electromagnetic current correlations in reduced quantum electrodynamics
• Note on an application of the method of uniqueness to reduced quantum electrodynamics
• Critical behaviour of ($2+1$)-dimensional QED: $1/N_f$-corrections in an arbitrary non-local gauge

Cited by in corpus (3)

• Landau-Khalatnikov-Fradkin transformation in three-dimensional quenched QED
• Four-loop singularities of the massless fermion propagator in quenched three-dimensional QED
• Critical properties of three-dimensional many-flavour QEDs