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

TL;DR

This paper investigates the (2+1)-dimensional Thirring model using large-N expansion, revealing a non-perturbative UV fixed point where fermions acquire parity-violating mass without inducing a Chern-Simons term.

Contribution

It provides an exact analysis of the UV fixed point and beta function in the large-N limit, showing parity-preserving symmetry breaking with dynamically generated fermion mass.

Findings

Fermions acquire parity-violating mass dynamically.

No Chern-Simons term is induced at any order.

Identifies a non-perturbative UV fixed point at lpha_c.

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 $\alpha$, $0 \leq \alpha \leq \alpha_c \equiv {1\over16} {\rm exp} (- {N \pi^2 \over 16})$. 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 $1/N$. $\alpha_c$ turns out to be a non-perturbative UV-fixed point in $1/N$. The $\beta$ function is calculated to be $\beta (\alpha) = -2 (\alpha - \alpha_c)$ near the fixed point, and the UV-fixed point and the $\beta$ function are shown exact in the $1/N$ expansion.