Ultraviolet Divergences in1NExpansions of Quantum Field Theories

For asymptotically free theories, ultraviolet divergences computed in the $\frac{1}{N}$ expansion with dimensional regularization reduce to simple poles plus powers of $\ln \epsilon$ or finite terms. The theories are effectively superrenormalizable since all divergences are determined by the one- and two-loop perturbative renormalization-group functions.