Dynamical Chiral Symmetry Breaking in Unquenched ${QED}_3$

Abstract

We investigate dynamical chiral symmetry breaking in unquenched ${QED}_3$ using the coupled set of Dyson--Schwinger equations for the fermion and photon propagators. For the fermion-photon interaction we employ an ansatz which satisfies its Ward--Green--Takahashi identity. We present self-consistent analytical solutions in the infrared as well as numerical results for all momenta. In Landau gauge, we find a phase transition at a critical number of flavours of $N_f^{\mathrm{c}rit}\approx 4$. In the chirally symmetric phase the infrared behaviour of the propagators is described by power laws with interrelated exponents. For $N_f=1$ and $N_f=2$ we find small values for the chiral condensate in accordance with bounds from recent lattice calculations. We investigate the Dyson--Schwinger equations in other linear covariant gauges as well. A comparison of their solutions to the accordingly transformed Landau gauge solutions shows that the quenched solutions are approximately gauge covariant, but reveals a significant amount of violation of gauge covariance for the unquenched solutions.

arXiv comment33 pages, 8 figures, reference added, version to be published in Phys. Rev. D

References in corpus (34)

• Dyson-Schwinger Equations and the Application to Hadronic Physics
• The Infrared Behavior of QCD Green's Functions - Confinement, Dynamical Symmetry Breaking, and Hadrons as Relativistic Bound States
• The Infrared Behavior of Gluon and Ghost Propagators in Landau Gauge QCD
• On the Infrared Exponent for Gluon and Ghost Propagation in Landau Gauge QCD
• A Solution to Coupled Dyson-Schwinger Equations for Gluons and Ghosts in Landau Gauge
• Non-perturbative Propagators, Running Coupling and Dynamical Quark Mass of Landau gauge QCD
• Conformal Phase Transition in Gauge Theories
• 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
• Infrared Exponents and Running Coupling of SU(N) Yang-Mills Theories
• Confinement and complex singularities in QED3
• QED3 theory of underdoped high temperature superconductors
• The Influence of the Full Vertex and Vacuum Polarization on the Fermion Propagator in QED3
• The Elusiveness of Infrared Critical Exponents in Landau Gauge Yang--Mills Theories
• Antiferromagnetism from phase disordering of a d-wave superconductor
• Quark-gluon vertex in arbitrary gauge and dimension
• ONE LOOP QED VERTEX IN ANY COVARIANT GAUGE: ITS COMPLETE ANALYTIC FORM
• Non-Compact QED_3 with N_f=1 and N_f=4
• Running Coupling in Non-Perturbative QCD - I. Bare Vertices and y-max Approximation
• 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
• QCD in the Infrared with Exact Angular Integrations
• Time-independant stochastic quantization, DS equations, and infrared critical exponents in QCD
• Gauge covariant fermion propagator in quenched, chirally-symmetric quantum electrodynamics
• Gauge covariance and the fermion-photon vertex in three- and four- dimensional, massless quantum electrodynamics
• The non-perturbative three-point vertex in massless quenched QED and perturbation theory constraints
• (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
• Landau-Khalatnikov-Fradkin Transformations and the Fermion Propagator in Quantum Electrodynamics
• Infrared cutoff dependence of the critical flavor number in three-dimensional QED
• Does the weak coupling limit of the Burden-Tjiang deconstruction of the massless quenched QED3 vertex agree with perturbation theory?
• Constructing the fermion-boson vertex in QED3
• Gauge Dependence of Mass and Condensate in Chirally Asymmetric Phase of Quenched QED3
• The nonperturbative propagator and vertex in massless quenched QED_d

Cited by in corpus (90)

• On the infrared behavior of Landau gauge Yang-Mills theory
• QCD at finite temperature and chemical potential from Dyson-Schwinger equations
• Fermion Interactions and Universal Behavior in Strongly Interacting Theories
• RG Flows and Bifurcations
• On the Phase Structure of Many-Flavor QED${}_3$
• Regarding confinement and dynamical chiral symmetry breaking in QED3
• Chiral Symmetry Breaking, Deconfinement and Entanglement Monotonicity
• Optical Lattice Hamiltonians for Relativistic Quantum Electrodynamics
• Dynamical quark mass generation in a strong external magnetic field
• Anomalous dimensions of monopole operators in three-dimensional quantum electrodynamics
• UV fixed-point structure of the three-dimensional Thirring model
• Chiral symmetry breaking in ${\mathrm{QED}}_3$ in presence of irrelevant interactions: a renormalization group study
• Critical behavior of the (2+1)-dimensional Thirring model
• Chiral symmetry breaking in three-dimensional quantum electrodynamics as fixed point annihilation
• Phase diagram of electronic systems with quadratic Fermi nodes in $2<d<4$: $2+\epsilon$ expansion, $4-\epsilon$ expansion, and functional renormalization group
• Beyond Miransky Scaling
• On $C_J$ and $C_T$ in Conformal QED
• Fermi velocity renormalization and dynamical gap generation in graphene
• Truncated Schwinger-Dyson Equations and Gauge Covariance in QED3
• Transverse Takahashi Identities and Their Implications for Gauge Independent Dynamical Chiral Symmetry Breaking
• Excitonic instability of three-dimensional gapless semiconductors: Large-N theory
• Bootstrapping $N_f=4$ conformal QED${}_3$
• Critical behaviour of ($2+1$)-dimensional QED: 1/N_f-corrections in the Landau gauge
• Fermion-induced quantum critical points in two-dimensional Dirac semimetals
• Excitonic pairing and insulating transition in two-dimensional semi-Dirac semimetals
• Quantum electrodynamics in 2+1 dimensions, confinement, and the stability of U(1) spin liquids
• Critical behaviour of ($2+1$)-dimensional QED: $1/N_f$-corrections in an arbitrary non-local gauge
• Phase transition and critical behavior of d=3 chiral fermion models with left/right asymmetry
• Spontaneous breaking of Lorentz symmetry in $(2+\epsilon )$-dimensional QED
• Massive Dirac fermions and the zero field quantum Hall effect
• Two dimensional metallic phases from disordered QED${}_3$
• Many-flavor Phase Diagram of the (2+1)d Gross-Neveu Model at Finite Temperature
• Landau-Khalatnikov-Fradkin transformations in Reduced Quantum Electrodynamics
• Non-perturbative beta function in three-dimensional electrodynamics
• Finite volume effects and dynamical chiral symmetry breaking in QED3
• Dynamical gap generation in graphene with frequency dependent renormalization effects
• Comments on the Chern-Simons photon term in the QED description of graphene
• Magnetic monopole plasma phase in (2+1)d compact quantum electrodynamics with fermionic matter
• Two infrared Yang-Mills solutions in stochastic quantization and in an effective action formalism
• Fermion and Photon gap-equations in Minkowski space within the Nakanishi Integral Representation method
• Chiral Symmetry breaking in Three Dimensional QED
• Gauge Covariance Relations and the Fermion Propagator in Maxwell-Chern-Simons QED3
• Landau-Khalatnikov-Fradkin transformation in three-dimensional quenched QED
• QED${}_3$ on a space-time lattice: compact versus noncompact formulation
• Dynamical chiral symmetry breaking in QED${}_3$ at finite density and impurity potential
• Continuum study of various susceptibilities within thermal QED${}_3$
• Confinement in Maxwell-Chern-Simons Planar Quantum Electrodynamics and the 1/N approximation
• Constructing Scalar-Photon Three Point Vertex in Massless Quenched Scalar QED
• Conformality and self-duality of $N_f=2$ QED${}_3$
• QED3 at Finite Temperature and Density
• Influence of gauge boson mass on the staggered spin susceptibility
• Unconventional behavior of Dirac fermions in three-dimensional gauge theory
• Nature of chiral phase transition in QED${}_3$ at zero density
• Parity Symmetry in QED3
• Effects of Anisotropy in QED3 from Dyson-Schwinger equations in a box
• Effects of random potentials in three-dimensional quantum electrodynamics
• Field theoretic study of electron-electron interaction effects in Dirac liquids
• Chiral symmetry breaking and monopole dynamics in non-compact QED3 coupled to a four-fermi interaction
• Dyson-Schwinger approach to strongly coupled theories
• The Podolsky propagator in gap and bound-state equations
• Confinement induced by fermion damping in three-dimensional QED
• Aspects of the pseudo Chiral Magnetic Effect in 2D Weyl-Dirac Matter
• Conformal field theory and the hot phase of three-dimensional U(1) gauge theory
• Critical scaling of finite temperature QED_3 in anisotropic space-time
• Endemic Infrared Divergences in QED3 at Finite Temperature
• Four-loop singularities of the massless fermion propagator in quenched three-dimensional QED
• Gauge dependence of the infrared behaviour of massless QED_3
• Infrared behavior of dynamical fermion mass generation in QED${}_3$
• Instability in scalar channel of fermion-antifermion scattering amplitude in massless QED_3 and anomalous dimensions of composite operators
• Calculation of the staggered spin correlation in the framework of the Dyson-Schwinger approach
• Looking at QED with Dyson-Schwinger equations: basic equations, Ward-Takahashi identities and the two-photon-two-fermion irreducible vertex
• Robustness of the semimetal state of Na3Bi and Cd3As2 against Coulomb interaction
• Asymptotic Infrared Fractal Structure of the Propagator for a Charged Fermion
• Anomalous magnetic moment in parity-conserving QED3
• Pauli-Term-Induced Fixed Points in $d$-dimensional QED
• Fate of superconductivity in disordered Dirac and semi-Dirac semimetals
• Renormalization of fermion velocity in finite temperature QED_{3}
• Gauge covariant solution for the Schwinger-Dyson equation in three-dimensional QED with Chern-Simons term
• Effects of Anisotropy in (2+1)-dimensional QED
• Chiral Symmetry Breaking and confinement in Minkowski space QED2+1
• Discussion for the Solutions of Dyson-Schwinger Equations at m>0 in QED3
• Stability of $SU(N_c)$ QCD3 from the $\epsilon$-Expansion
• Critical properties of three-dimensional many-flavour QEDs
• Physics-informed neural networks viewpoint for solving the Dyson-Schwinger equations of quantum electrodynamics
• $\mathcal{N}=1$ supersymmetric three-dimensional QED in the large-$N_f$ limit and applications to super-graphene
• Determination of the propagator in QED3 by spectral function
• Critical number of fermions in three-dimensional QED
• Vortex driven phase transition in Topologically Massive QED
• Influence of Fermion Velocity Renormalization on Dynamical Mass Generation in QED${}_3$
• Planar generalized electrodynamics for one-loop amplitude in the Heisenberg picture