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Thirring Model as a Gauge Theory

High Energy Physics - Theory 2009-10-28 v2 High Energy Physics - Lattice High Energy Physics - Phenomenology

Abstract

We reformulate the Thirring model in DD (2D<4)(2 \le D < 4) dimensions as a gauge theory by introducing U(1)U(1) hidden local symmetry (HLS) and study the dynamical mass generation of the fermion through the Schwinger-Dyson (SD) equation. By virtue of such a gauge symmetry we can greatly simplify the analysis of the SD equation by taking the most appropriate gauge (``nonlocal gauge'') for the HLS. In the case of even-number of (2-component) fermions, we find the dynamical fermion mass generation as the second order phase transition at certain fermion number, which breaks the chiral symmetry but preserves the parity in (2+1) dimensions (D=3D=3). In the infinite four-fermion coupling (massless gauge boson) limit in (2+1) dimensions, the result coincides with that of the (2+1)-dimensional QED, with the critical number of the 4-component fermion being Ncr=1283π2N_{\rm cr} = \frac{128}{3\pi^{2}}. As to the case of odd-number (2-component) fermion in (2+1) dimensions, the regularization ambiguity on the induced Chern-Simons term may be resolved by specifying the regularization so as to preserve the HLS. Our method also applies to the (1+1) dimensions, the result being consistent with the exact solution. The bosonization mechanism in (1+1) dimensional Thirring model is also reproduced in the context of dual-transformed theory for the HLS.

Keywords

Cite

@article{arxiv.hep-th/9411201,
  title  = {Thirring Model as a Gauge Theory},
  author = {Taichi Itoh and Yoonbai Kim and Masaki Sugiura and Koichi Yamawaki},
  journal= {arXiv preprint arXiv:hep-th/9411201},
  year   = {2009}
}

Comments

33 pages

R2 v1 2026-07-22T15:52:38.231Z