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

TL;DR

This paper analyzes the renormalization properties of the Thirring model in dimensions between 2 and 4 using 1/N_f expansion, demonstrating its renormalizability at O(1/N_f) and establishing a universal scattering amplitude.

Contribution

It provides explicit O(1/N_f) corrections and shows the model's renormalizability at this order, extending understanding of the Thirring model's behavior in higher dimensions.

Findings

No ultraviolet divergences at leading order with proper regularization.

Model is renormalizable at O(1/N_f) in the massless limit.

Universal amplitude for four-particle scattering in the asymptotic regime.

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.