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 $1/N$ 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, $N_c(\xi )$ where $\xi$ is the gauge fixing parameter, which is such that D$\chi$SB takes place for $N<N_c(\xi )$. Neglecting the weak gauge-dependent terms yields $N_c=2.8469$ while, in the general case, it is found that: $N_c(1)=3.0084$ in the Feynman gauge, $N_c(0)=3.0844$ in the Landau gauge and $N_c(2/3)=3.0377$ in the $\xi =2/3$ gauge where the leading order fermion wave function is finite. These results suggest that D$\chi$SB should take place for integer values $N\le 3$.

(v2) Accepted for publication in PRD. 8 pages, 2 figures; 2 references added. (v1) LaTeX file with feynMF package. 6 pages, 2 figures; includes Supplemental Material (3 pages). arXiv admin note: text overlap with arXiv:1605.01911

References in corpus (6)

• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• On the Phase Structure of Many-Flavor QED${}_3$
• Electromagnetic current correlations in reduced quantum electrodynamics
• Gauge invariance of a critical number of flavours in QED3
• Note on an application of the method of uniqueness to reduced quantum electrodynamics
• Two-loop fermion self-energy and propagator in reduced QED${}_{3,2}$

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• Addendum to "Critical behaviour of ($2+1$)-dimensional QED: $1/N_f$-corrections in an arbitrary non-local gauge"
• Conformal field theory and the hot phase of three-dimensional U(1) gauge theory
• Four-loop singularities of the massless fermion propagator in quenched three-dimensional QED
• Non-perturbative field theoretical aspects of graphene and related systems
• Critical properties of three-dimensional many-flavour QEDs
• Continuous order-to-order quantum phase transitions from fixed-point annihilation
• $\mathcal{N}=1$ supersymmetric three-dimensional QED in the large-$N_f$ limit and applications to super-graphene