LARGE-N ANALYSIS OF THE (2+1)-DIMENSIONAL THIRRING MODEL

We analyze the (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 less-than-or-equal-to alpha less-than-or-equal-to alpha(c) = 1/16 exp(-Npi2/16). 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 nouperturbative 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 to be exact in the 1/N expansion.