Thirring Model as a Gauge Theory

Abstract

We give another reformulation of the Thirring model (with four-fermion interaction of the current-current type) as a gauge theory and identify it with a gauge-fixed version of the corresponding gauge theory according to the Batalin-Fradkin formalism. Based on this formalism, we study the chiral symmetry breaking of the $D$-dimensional Thirring model ($2<D<4$) with $N$ flavors of 4-component fermions. By constructing the gauge covariant effective potential for the chiral order parameter, up to the leading order of $1/N$ expansion, we show the existence of the second order chiral phase transition and obtain explicitly the critical number of flavors $N_c$ (resp. critical four-fermion coupling $G_c$) as a function of the four-fermion coupling $G$ (resp. $N$), below (resp. above) which the chiral symmetry is spontaneously broken.

18 pages, LaTeX (revised final version, to be published in Nucl. Phys. B)

References in corpus (7)

• First-order Phase Transition in Three-dimensional QED with Chern--Simons Term
• Thirring Model as a Gauge Theory
• Dynamical Breakdown of Chirality and Parity in (2+1)-dimensional QED
• Large-N analysis of (2+1)-dimensional Thirring model
• Gaussian approximation of the (2+1) dimensional Thirring model in the functional Schrödinger picture
• A Parity Invariant Regularization in 3-D Quantum Electrodynamics
• Flavor-Dependence and Higher Orders of Gauge-Independent Solutions in Strong Coupling Gauge Theory

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• On the Phase Structure of Many-Flavor QED${}_3$
• Abelian-Projected Effective Gauge Theory of QCD with Asymptotic Freedom and Quark Confinement
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• Critical behavior of the (2+1)-dimensional Thirring model
• Fixed-point structure of low-dimensional relativistic fermion field theories: Universality classes and emergent symmetry
• The Three Dimensional Thirring Model for Small N_f
• Critical flavour number of the Thirring model in three dimensions
• The Three Dimensional Thirring Model for N_f=4 and N_f=6
• Monte Carlo Simulation of the Three Dimensional Thirring Model
• Many-flavor Phase Diagram of the (2+1)d Gross-Neveu Model at Finite Temperature
• Abelian Chern-Simons-Maxwell theory from a tight binding model of spinless fermions
• Momentum dependence of quantum critical Dirac systems
• Absence of chiral symmetry breaking in Thirring models in 1+2 dimensions
• Bosonization of Thirring Model in Arbitrary Dimension
• Theory of spin response in underdoped cuprates as strongly fluctuating d-wave superconductors
• Symmetries of Thirring models on 3d lattices
• Finite Field-dependent Symmetry in Thirring Model
• Gauged Thirring Model in the Heisenberg Picture
• Strong coupling limits and quantum isomorphisms of the gauged Thirring model
• Magnetization and dynamically induced finite densities in three-dimensional Chern-Simons QED
• Nonperturbative Aspects of the two-dimensional Massive Gauged Thirring Model
• Electroweak symmetry breaking in other terms
• Chiral Symmetry Breaking in 2+1 dimensions due to Sphalerons