Critical behavior of (2+1)-dimensional QED:1/Nfcorrections in an arbitrary nonlocal gauge

Abstract

Dynamical chiral symmetry breaking (DχSB) is studied within (2 + 1)-dimensional QED with N four-component fermions. The leading and next-to-leading orders of the 1/N expansion are computed exactly. The analysis is carried out in an arbitrary non-local gauge. Resumming the wave-function renormalization constant at the level of the gap equation yields a strong suppression of the gauge dependence of the critical fermion flavour number, Nc(ξ) where ξ is the gauge fixing parameter, which is such that DχSB takes place for N < Nc(ξ). Neglecting the weak gaugedependent terms yields Nc = 2.8469 while, in the general case, it is found that: Nc(1) = 3.0084 in the Feynman gauge, Nc(0) = 3.0844 in the Landau gauge and Nc(2/3) = 3.0377 in the ξ = 2/3 gauge where the leading order fermion wave function is finite. These results suggest that DχSB should take place for integer values N ≤ 3.

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“…Figure 6: Examples of complicated diagrams appearing in Refs. [134,135]. technique) involve explicit integrations.…”

“…In some cases, one may expect that simpler expressions may be obtained, e.g., in the case of the diagrams of Fig. 6 which appear in the study of three-dimensional QED [134,135]. Though this task has not been carried out explicitly yet, it has been shown in [134] that the Gegenbauer polynomial technique, see Sec.…”

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“…In another context, this kind of diagram was computed exactly: see diagram 1 in figure 2 of ref. [46] together with eqs. (19) and (20) in this reference as well as the sentence below eq.…”

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