We consider the most general renormalizable chiral Yukawa model with $SU(3)_{ \rm color}$ replaced by $SU(N_c)$, $SU(2)_{ \rm L}$ replaced by $SU(N_w )$ and $U(1)_{ Y}$ replaced by $U(1)^{ N_w -1}$ in the limit $N_c \rightarrow\infty$, $N_w \rightarrow\infty$ with the ratio $\rho=\sqrt{ { N_w}\over{ N_c}} \ne 0,\infty$ 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 $m_t \le 1~TeV$.
Categories: hep-lat hep-ph