CHIRAL YUKAWA MODELS IN THE PLANAR LIMIT

We consider the most general renormalizable chiral Yukawa model with SU(3)color replaced by SU(N(c)), SU(2)L replaced by SU(N(w)) and U(1)Y replaced by U(1)Nw-1 in the limit N(c) --> infinity, N(w) --> infinity with the ratio rho=square-root N(w)/N(c) not-equal 0, infinity held fixed. Since for N(w)greater-than-or-equal-to 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) less-than-or-equal-to 1 TeV.