Chiral symmetry breaking in ${\mathrm{QED}}_3$ in presence of irrelevant interactions: a renormalization group study

Abstract

Motivated by recent theoretical approaches to high temperature superconductivity, we study dynamical mass generation in three dimensional quantum electrodynamics ${\mathrm{QED}}_3$) in presence of irrelevant four-fermion quartic terms. The problem is reformulated in terms of the renormalization group flows of certain four-fermion couplings and charge, and then studied in the limit of large number of fermion flavors $N$. We find that the critical number of fermions $N_c$ below which the mass becomes dynamically generated depends continuously on a weak chiral-symmetry-breaking interaction. One-loop calculation in our gauge-invariant approach yields $N_{c0}=6$ in pure ${\mathrm{QED}}_3$. We also find that chiral-symmetry-preserving mass cannot become dynamically generated in pure ${\mathrm{QED}}_3$.

arXiv comment7 pages, 7 figures

References in corpus (19)

• QED3 theory of pairing pseudogap in cuprates: From d-wave superconductor to antiferromagnet via "algebraic" Fermi liquid
• Algebraic Fermi liquid from phase fluctuations: "topological" fermions, vortex "berryons" and QED3 theory of cuprate superconductors
• QED3 theory of underdoped high temperature superconductors
• A New Constraint on Strongly Coupled Field Theories
• The Influence of the Full Vertex and Vacuum Polarization on the Fermion Propagator in QED3
• Antiferromagnetism from phase disordering of a d-wave superconductor
• Dynamical Chiral Symmetry Breaking in Unquenched ${QED}_3$
• Non-Compact QED_3 with N_f=1 and N_f=4
• Non-compact QED_3 with N_f >=2
• Chiral Symmetry Breaking and Phase Fluctuations in Cuprate Superconductors: A QED${}_3$ Unified Theory of the Pseudogap State
• Relativity Restored: Dirac Anisotropy in QED${}_3$
• Infrared cutoff dependence of the critical flavor number in three-dimensional QED
• The effect of velocity anisotropy on the antiferromagnetic instability of a d-wave superconductor
• O(1/N_f) Corrections to the Thirring Model in 2<d<4
• Large-N analysis of (2+1)-dimensional Thirring model
• Fine structure of chiral symmetry breaking in the $QE{D}_3$ theory of underdoped high-$T_c$ superconductors
• Theory of spin response in underdoped cuprates as strongly fluctuating d-wave superconductors
• ERG and Schwinger-Dyson Equations - Comparison in formulations and applications --
• Theory of strongly phase fluctuating d-wave superconductors and the spin response in underdoped cuprates

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