O(1/Nf) corrections to the Thirring model in 2<d<4

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/${\mathit{N}}_{\mathit{f}}$ expansion, where ${\mathit{N}}_{\mathit{f}}$ 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/${\mathit{N}}_{\mathit{f}}$) corrections are computed, and the model is 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 that there is a universal amplitude for four particle scattering in the asymptotic regime. Comparisons are made with both the Gross-Neveu model and QED.