THE NAMBU-JONA-LASINIO MODEL AND GAUGE-THEORIES IN 2+1 DIMENSIONS

The weakly coupled globally invariant Nambu-Jona-Lasino (NJL) model in 2 + 1 dimensions is shown to be equivalent to a strongly coupled gauge theory. This equivalence is demonstrated for the renormalized theories in the 1/N expansion utilizing an unconventional, cutoff-dependent bare coupling constant to take the limit of weak or strong bare couplings. The weakly coupled Abelian NJL model is renormalized to order 1/N and compared to a renormalized strongly coupled QED3. Next, the U(2) globally invariant NJL model is studied in the broken phase and renormalized to leading order. The resulting U(1) x U(1) guage-invariant theory is shown to be equivalent to a spontaneously broken U(2) gauge theory analyzed in the 1/N expansion.