For unitary matrix models with potentials up to cos 3α, the paper infers phase diagrams from classical potential shape and shows beta functions on critical lines are nowhere vanishing, claiming third-order transitions.
Renormalization Group Flow near the Superconformal Points in N=2 Supersymmetric Gauge Theories
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abstract
The behavior of the beta-function of the low-energy effective coupling in the N=2 supersymmetric SU(2) QCD with several massive matter hypermultiplets and in the SU(3) Yang-Mills theory is determined near the superconformal points in the moduli space. The renormalization group flow is unambiguously fixed by looking at limited types of deformation near the superconformal points. It is pointed out that the scaling dimension of the beta-function is controlled by the scaling behavior of moduli parameters and the relation between them is explicitly worked out. Our scaling dimensions of the beta-functions are consistent in part with the results obtained recently by Bilal and Ferrari in a different method for the SU(2) QCD.
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Notes on phase structure and non-vanishing $\beta$ functions of one-unitary matrix model
For unitary matrix models with potentials up to cos 3α, the paper infers phase diagrams from classical potential shape and shows beta functions on critical lines are nowhere vanishing, claiming third-order transitions.