RENORMALIZATION OF THE BROKEN-SYMMETRY TWO-DIMENSIONAL SU(N) SIGMA-MODEL AND (PSI-PSI)2 MODEL

We derive the renormalized Schwinger-Dyson equations for the two-dimensional SU(N) model with N i and one and the (ii)2 model with spontaneously broken symmetry 0. We study the model in the composite limit when the wave-function renormalization constant Z3 and the 4- vertex renormalization constant Z4 are zero and find that the renormalized Green's functions of the model become identical to those of the ()2 model. In the composite limit of the model the renormalized coupling constants g» and 4 are related and become calculable in terms of the spontaneously generated fermion mass. We obtain the renormalized gap equation for M2r which determines the minimum of the effective potential and discuss the Callan-Symanzik equations for the broken-symmetry sector of these models. We show that the Z3=Z4=0 limit of the model is obtained at the fixed point =0 of the Callan-Symanzik equations. © 1979 The American Physical Society.