Large-N analysis of (2+1)-dimensional Thirring model

Abstract

We analyze $(2+1)$-dimensional vector-vector type four-Fermi interaction (Thirring) model in the framework of the $1/N$ expansion. By solving the Dyson-Schwinger equation in the large-$N$ limit, we show that in the two-component formalism the fermions acquire parity-violating mass dynamically in the range of the dimensionless coupling $α$, $0 \leq α\leq α_c \equiv {1\over16} {\rm exp} (- {N π^2 \over 16})$. The symmetry breaking pattern is, however, in a way to conserve the overall parity of the theory such that the Chern-Simons term is not induced at any orders in $1/N$. $α_c$ turns out to be a non-perturbative UV-fixed point in $1/N$. The $β$ function is calculated to be $β(α) = -2 (α- α_c)$ near the fixed point, and the UV-fixed point and the $β$ function are shown exact in the $1/N$ expansion.