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Theory space of one unitary matrix model and its critical behavior associated with Argyres-Douglas theory
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abstract
The lowest critical point of one unitary matrix model with cosine plus logarithmic potential is known to correspond with the $(A_1, A_3)$ Argyres-Douglas (AD) theory and its double scaling limit derives the Painlev\'{e} II equation with parameter. Here, we consider the critical points associated with all cosine potentials and determine the scaling operators, their vevs and their scaling dimensions from perturbed string equations at planar level. These dimensions agree with those of $(A_1,A_{4k-1})$ AD theory.
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Cited by 2 Pith papers
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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.
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Phases and triple(multiple) point: critical phenomena around the AD singularity
For the L=2 one-unitary matrix model, the paper determines the phase separation lines, finds a triple point at (tau, lambda)=(1/8, 3/2), and identifies the 1-to-2 gap line as the k=2 multicritical line.
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