Critical behaviour of (2 + 1)-dimensional QED: 1/N f -corrections in an arbitrary non-local gauge

a V Kotikov (1) , S Teber (2)

1 BLTP - Bogoliubov Laboratory of Theoretical Physics [Dubna]
2 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

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 gauge-dependent 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. Introduction-We consider Quantum Electrodynamics in 2 + 1 dimensions (QED 3) which is described by the Lagrangian:

Domaines: Systèmes mésoscopiques et effet Hall quantique [cond-mat.mes-hall]

a V Kotikov, S Teber. Critical behaviour of (2 + 1)-dimensional QED: 1/N f -corrections in an arbitrary non-local gauge. 2016. ⟨hal-01370999⟩