Renormalization of scalar quartic and Yukawa couplings in unified gauge theories based onE 6

Renormalization group equations for scalar and Yukawa couplings in gauge theories based on the exceptional groupE ₆ are analyzed. Asymptotic freedom is possible only for a limited set of scalar fields, and then only if several fermion generations are present. The infrared behavior of the scalar quartic coupling constants is striking: they are necessarily driven out of the region of positivity of the classical potential. Some useful group theoretic relations inE ₆ are given in an Appendix.