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

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

1993-07-30

arxiv.org/abs/hep-th/9307186v2

Phys.Rev. D49 (1994) 5507-5511

Physics

High Energy Physics

High Energy Physics - Theory

14 pages Latex. (Revised version: some changes have been made and references added.) To appear in Phys. Rev. D, SNUTP 93-47

Scientific paper

10.1103/PhysRevD.49.5507

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.

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