Thirring Model as a Gauge Theory

We reformulate the Thirring model in D(2 ≤D ≪ 4) dimensions as a gauge theory by introducing 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 = 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 = 128/3π2. 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.