Large-N analysis of (2+1)-dimensional Thirring model

Abstract

We analyze $(2+1)$-dimensional vector-vector type four-Fermi interaction (Thirring) model in the framework of the $1/N$ expansion. By solving the Dyson-Schwinger equation in the large-$N$ limit, we show that in the two-component formalism the fermions acquire parity-violating mass dynamically in the range of the dimensionless coupling $\alpha$, $0\le \alpha \le {\alpha }_c\equiv \frac{1}{16}\exp (-\frac{N{\pi }^2}{16})$. The symmetry breaking pattern is, however, in a way to conserve the overall parity of the theory such that the Chern-Simons term is not induced at any orders in $1/N$. ${\alpha }_c$ turns out to be a non-perturbative UV-fixed point in $1/N$. The $\beta$ function is calculated to be $\beta (\alpha )=-2(\alpha -{\alpha }_c)$ near the fixed point, and the UV-fixed point and the $\beta$ function are shown exact in the $1/N$ expansion.

14 pages Latex. (Revised version: some changes have been made and references added.) To appear in Phys. Rev. D, SNUTP 93-47

References in corpus (2)

• A Tumbling Top-Quark Condensate Model
• The Effective Lagrangian of Three Dimensional Quantum Chromodynamics

Cited by in corpus (30)

• On the Phase Structure of Many-Flavor QED${}_3$
• Critical exponents of the semimetal-insulator transition in graphene: A Monte Carlo study
• 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
• Critical Flavor Number in the Three Dimensional Thirring Model
• The Three Dimensional Thirring Model for Small N_f
• O(1/N_f) Corrections to the Thirring Model in 2<d<4
• Unruh effect for interacting particles with ultracold atoms
• Thirring Model as a Gauge Theory
• Critical flavour number of the Thirring model in three dimensions
• Phase transition and critical behavior of d=3 chiral fermion models with left/right asymmetry
• The Three Dimensional Thirring Model for N_f=4 and N_f=6
• The Phase Diagram of the Three Dimensional Thirring Model
• Monte Carlo Simulation of the Three Dimensional Thirring Model
• Holographic aspects of three dimensional QCD from string theory
• Momentum dependence of quantum critical Dirac systems
• Dynamical Mass Generation in Pseudo Quantum Electrodynamics with Four-Fermion Interactions
• Gaussian approximation of the (2+1) dimensional Thirring model in the functional Schrödinger picture
• Symmetries of Thirring models on 3d lattices
• Finite Field-dependent Symmetry in Thirring Model
• Spontaneous non-Hermiticity in the (2+1)-dimensional Thirring model
• Bosonization of the Thirring Model in 2+1 Dimensions
• Hartree-Fock approach to dynamical mass generation in the generalized (2+1)-dimensional Thirring model
• Cascade of phase transitions in a planar Dirac material
• Four-Fermion Theories with Exact Chiral Symmetry in Three Dimensions
• The Dynamical Behaviors in (2+1)-Dimensional Gross-Neveu Model with a Thirring Interaction
• Renormalization of the optical band gap through an effective Thirring interaction for massive Dirac-like electrons
• Discrete Anomaly and Dynamical Mass in 2+1 dimensional $U(1{)}_V\times U(1{)}_A$ Model
• Chiral Symmetry Breaking in 2+1 dimensions due to Sphalerons