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Phases and triple(multiple) point: critical phenomena around the AD singularity
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abstract
Continuing with our previous series of work, we present a case study of the critical phenomena around Argyres-Douglas singularity of ${\cal N} =2$ susy made at $(A_1, A_{4k-1} ), k =1, 2$ realized by one-unitary matrix model. We determine the phase diagram, which is recast into LEEA of $\mathcal{N}=2$, 4d gauge theory by the 0d-4d connection. There are three distinct phases, each corresponding to an eigenvalue distribution with 0, 1, and 2 gaps. These form an entire phase diagram with a triple point. Examining the behavior of the planar free energy, we show, among other things,that the transition line between 1- and 2-gap phases ending at the triple point is the $k=2$ multicritical one.
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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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