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 $N\le 3$.

arXiv comment(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 (27)

• Electron-Electron Interactions in Graphene: Current Status and Perspectives
• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• A New Constraint on Strongly Coupled Field Theories
• Dynamical Chiral Symmetry Breaking in Unquenched ${QED}_3$
• Quantum Electrodynamics of Particles on a Plane and the Chern-Simons Theory
• Dynamical Chiral Symmetry Breaking on a Brane in Reduced QED
• Non-Compact QED_3 with N_f=1 and N_f=4
• The Gegenbauer Polynomial Technique: the evaluation of a class of Feynman diagrams
• On the Phase Structure of Many-Flavor QED${}_3$
• Electromagnetic current correlations in reduced quantum electrodynamics
• Scale-invariance of parity-invariant three-dimensional QED
• Gauge invariance of a critical number of flavours in QED3
• Quantum Electrodynamics in d=3 from the epsilon-expansion
• No evidence for bilinear condensate in parity-invariant three-dimensional QED with massless fermions
• Chiral symmetry breaking in three-dimensional quantum electrodynamics as fixed point annihilation
• Two-loop fermion self-energy in reduced quantum electrodynamics and application to the ultra-relativistic limit of graphene
• On $C_J$ and $C_T$ in Conformal QED
• Electron Mass Anomalous Dimension at O(1/N^2_f) in Quantum Electrodynamics
• (2+1)-Dimensional QED with Dynamically Massive Fermions in the Vacuum Polarization
• Computation of Critical Exponent Eta at O(1/N_f^2) in Quantum Electrodynamics in Arbitrary Dimensions
• Nonperturbative infrared dynamics of three-dimensional QED with a four-fermion interaction
• 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 the Landau gauge
• Spontaneous breaking of Lorentz symmetry in $(2+\epsilon )$-dimensional QED
• Landau-Khalatnikov-Fradkin transformations in Reduced Quantum Electrodynamics
• Two-loop fermion self-energy and propagator in reduced QED${}_{3,2}$
• On the critical behavior of (2+1)-dimensional QED

Cited by in corpus (17)

• Multi-loop techniques for massless Feynman diagram calculations
• Critical behavior of the QED${}_3$-Gross-Neveu model: Duality and deconfined criticality
• QED${}_3$ with quenched disorder: quantum critical states with interactions and disorder
• Confinement transition in the QED${}_3$-Gross-Neveu-XY universality class
• Two dimensional metallic phases from disordered QED${}_3$
• Fermion bilinear operator critical exponents at $O(1/N^2)$ in the QED-Gross-Neveu universality class
• Landau-Khalatnikov-Fradkin transformation in three-dimensional quenched QED
• The effect of a Chern-Simons term on dynamical gap generation in graphene
• Addendum to "Critical behaviour of ($2+1$)-dimensional QED: $1/N_f$-corrections in an arbitrary non-local gauge"
• Field theoretic study of electron-electron interaction effects in Dirac liquids
• 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
• New results for a two-loop massless propagator-type Feynman diagram
• Continuous order-to-order quantum phase transitions from fixed-point annihilation
• Critical properties of three-dimensional many-flavour QEDs
• $\mathcal{N}=1$ supersymmetric three-dimensional QED in the large-$N_f$ limit and applications to super-graphene