Asymptotically Free versus Asymptotically Non-Free Gauge Theories

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Abstract
Using the solutions of improved planar Schwinger-Dyson equation, the renormalization flow and fixed point structure are studied for the QCD like gauge theories. Two types of the ultraviolet fixed points are observed in the 2-parameter plane, (\tildeλ, \tildeA), the strength (\tildeλ) and the rapidness of the running coupling constant (\tildeA). One type corresponds to the so-called trivial ultraviolet fixed point observed in asymptotically free gauge theories, and the other to the nontrivial ulltraviolet fixed point to which much attention has been paid from both theoretical and phenomenological points of view. Those two types of fixed points exhibit significantly different properties in some important respects.

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