O(1/N_f) Corrections to the Thirring Model in 2<d<4

Abstract

The Thirring model, that is, a relativistic field theory of fermions with a contact interaction between vector currents, is studied for dimensionalities 2<d<4 using the 1/N_f expansion, where N_f is the number of fermion species. The model is found to have no ultraviolet divergences at leading order provided a regularization respecting current conservation is used. Explicit O(1/N_f) corrections are computed, and the model shown to be renormalizable at this order in the massless limit; renormalizability appears to hold to all orders due to a special case of Weinberg's theorem. This implies there is a universal amplitude for four particle scattering in the asymptotic regime. Comparisons are made with both the Gross-Neveu model and QED.

22 pages in plain TeX, with 7 figs included using psfig.tex (Minor conceptual changes - algebra unaffected)

References in corpus (8)

• Four - Fermi Theories in Fewer Than Four Dimensions
• Computation of Critical Exponent ηat O(1/N^3) in the Four Fermi Model in Arbitrary Dimensions
• Critical Behaviour of the 3d Gross-Neveu and Higgs-Yukawa Models
• Computation of $\beta (g_c)$ at O(1/N^2) in the O(N) Gross Neveu Model in Arbitrary Dimensions
• Electron Mass Anomalous Dimension at O(1/N^2_f) in Quantum Electrodynamics
• Computation of Critical Exponent Eta at O(1/N_f^2) in Quantum Electrodynamics in Arbitrary Dimensions
• Large-N analysis of (2+1)-dimensional Thirring model
• Algorithm for Computing the $\BETA$-Function of Quantum Electrodynamics in the Large N_f Expansion

Cited by in corpus (32)

• The QCD beta-function at O(1/N_f)
• SL(2,Z) Action on Three-Dimensional CFTs and Holography
• Non-Compact QED_3 with N_f=1 and N_f=4
• The fermion bag approach to lattice field theories
• Quantum critical behavior in three dimensional lattice Gross-Neveu models
• 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
• 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 Flavor Number in the Three Dimensional Thirring Model
• An asymptotic safety scenario for gauged chiral Higgs-Yukawa models
• Gravitational Duality Transformations on (A)dS4
• On the exact quantum scale invariance of three-dimensional reduced QED theories
• Critical flavour number of the Thirring model in three dimensions
• The Phase Diagram of the Three Dimensional Thirring Model
• The Three Dimensional Thirring Model for N_f=4 and N_f=6
• Monte Carlo Simulation of the Three Dimensional Thirring Model
• On the Critical Flavor Number in the 2+1$d$ Thirring Model
• Momentum dependence of quantum critical Dirac systems
• Absence of chiral symmetry breaking in Thirring models in 1+2 dimensions
• Critical Behaviour in the Single Flavor Thirring Model in 2+1d
• Chiral symmetry breaking and monopole dynamics in non-compact QED3 coupled to a four-fermi interaction
• Spontaneous non-Hermiticity in the (2+1)-dimensional Thirring model
• The relevance of the three dimensional Thirring coupling at finite temperature and density
• Bosonization of the Thirring Model in 2+1 Dimensions
• Fermion bag solutions to some sign problems in four-fermion field theories
• Hartree-Fock approach to dynamical mass generation in the generalized (2+1)-dimensional Thirring model
• Large N Thirring Matter in Three Dimensions
• Critical Behaviour in the Single Flavor Thirring Model in 2+1$d$ with Wilson Kernel Domain Wall Fermions
• Transition in the spectral gap of the massless overlap Dirac operator coupled to abelian fields in three dimensions
• Massless Three Dimensional Quantum Electrodynamics and Thirring Model Constrained by Large Flavor Number