Perturbation of multi-critical unitary matrix models, double scaling limits, and Argyres-Douglas theories. (English) Zbl 1489.81051
Summary: Using the saddle point method, we give an explicit form of the planar free energy and Wilson loops of unitary matrix models in the one-cut regime. The multi-critical unitary matrix models are shown to undergo third-order phase transitions at two points by studying the planar free energy. One of these ungapped/gapped phase transitions is multi-critical, while the other is not multi-critical. The spectral curve of the \(k\)-th multi-critical matrix model exhibits an \(A_{4k - 1}\) singularity at the multi-critical point. Perturbation around the multi-critical point and its double scaling limit are studied. In order to take the double scaling limit, the perturbed coupling constants should be fine-tuned such that all the zero points of the spectral curve approach to the \(A_{4k - 1}\) singular point. The fine-tuning is examined in the one-cut regime, and the scaling behavior of the perturbed couplings is determined. It is shown that the double scaling limit of the spectral curve is isomorphic to the Seiberg-Witten curve of the Argyres-Douglas theory of type \((A_1, A_{4 k - 1})\).
MSC:
| 81T32 | Matrix models and tensor models for quantum field theory |
| 81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
| 81T18 | Feynman diagrams |
| 82C26 | Dynamic and nonequilibrium phase transitions (general) in statistical mechanics |
| 82C35 | Irreversible thermodynamics, including Onsager-Machlup theory |
| 47A25 | Spectral sets of linear operators |
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