Chiral Yukawa models in the planar limit

Abstract

We consider the most general renormalizable chiral Yukawa model with $SU(3{)}_{\mathrm{color}}$ replaced by $SU(N_c)$, $SU(2{)}_{\mathrm{L}}$ replaced by $SU(N_w)$ and $U(1{)}_Y$ replaced by $U(1{)}^{N_w-1}$ in the limit $N_c\to \infty$, $N_w\to \infty$ with the ratio $\rho =\sqrt{\frac{N_w}{N_c}}\ne 0,\infty$ held fixed. Since for $N_w\ge 3$ only one renormalizable Yukawa coupling per family exists and there is no mixing between families the limit is appropriate for the description of the effects of a heavy top quark when all the other fermions are taken to be massless. A rough estimate of the triviality bound on the Yukawa coupling is equivalent to $m_t\le 1TeV$.

Comments: 8p, one postscript figure appended, RU-92-20