The effective potential and the bound states for a class of two dimensional gauge theories

The effective potential is calculated for a two dimensionalU(N) gauge theory with scalar quarks to leading order in the 1/N expansion. If there is noφ ⁴ interaction present, the potential is unbounded from below. If theφ ⁴ interaction is present, the potential is bounded from below and there is an unbroken and a spontaneously broken symmetry phase. The bound state spectrum of the unbroken phase is very similar to that of anU(N) gauge theory without theφ ⁴ term.