Multiple phases and meromorphic deformations of unitary matrix models

Santilli, Leonardo; Tierz, Miguel

doi:10.48550/arxiv.2102.11305

Cited by 3 publications

(3 citation statements)

References 72 publications

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“…It was considered in [37] without a logarithmic potential. (For the recent development about the phase structures of a generalized GWW model, see [38].…”

Section: Introductionmentioning

confidence: 99%

Theory space of one unitary matrix model and its critical behavior associated with Argyres-Douglas theory

Itoyama,

Yano

2021

Preprint

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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 Painlevé 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

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“…It was considered in [37] without a logarithmic potential. (For the recent development about the phase structures of a generalized GWW model, see [38].…”

Section: Introductionmentioning

confidence: 99%

Theory space of one unitary matrix model and its critical behavior associated with Argyres-Douglas theory

Itoyama,

Yano

2021

Preprint

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“…It is known that the unitary matrix models with general coupling have many phases [73,74,75,76,77]. We have considered the multi-critical models with real coupling g, and showed that they have three phases.…”

Section: Discussionmentioning

confidence: 97%

Perturbation of multi-critical unitary matrix models, double scaling limits, and Argyres-Douglas theories

Oota

2021

Preprint

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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 finetuned 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 4k−1 ).

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“…In the series of developments on the irregular limit of the A 1 (one-matrix) case [35][36][37][38][39][40][41], we have been led to the procedure of converting the hermitean matrix model into the unitary matrix model in order to make such procedure well-defined. The upshot from the case of N f = 2 is the well-known GWW model [42][43][44][45] (see also [46][47][48][49] for recent discussion) augmented by the log potential. The Painlevé II equation with parameter has been derived in the double scaling limit [35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Construction of irregular conformal/W block and flavor mass relations of $\mathcal{N}=2$ SUSY gauge theory from the $A_{n-1}$ quiver matrix model

Itoyama¹,

Oota²,

Yoshioka³

2022

Preprint

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A sequence of massive scaling limits of the β-deformed A n−1 quiver matrix model that keeps the size of the matrices finite and that corresponds to the N f = 2n → 2n − 1, 2n − 2 limits on the number of flavors at 4d su(n) N = 2 SUSY gauge theory side is carried out to provide us with the integral representation of su(n) irregular conformal/W block. The original paths are naturally deformed into those in the complex plane, permitting us to convert into an su(n) extension of the unitary matrix model of GWW type with a set of log potentials for all species of eigenvalues. Looking at the region in the parameter space that enjoys the maximal symmetry of the model, we derive a set of relations among the mass parameters which may serve as evidence for the existence of the Argyres-Douglas critical hypersurface.

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Multiple phases and meromorphic deformations of unitary matrix models

Cited by 3 publications

References 72 publications

Theory space of one unitary matrix model and its critical behavior associated with Argyres-Douglas theory

Theory space of one unitary matrix model and its critical behavior associated with Argyres-Douglas theory

Perturbation of multi-critical unitary matrix models, double scaling limits, and Argyres-Douglas theories

Construction of irregular conformal/W block and flavor mass relations of $\mathcal{N}=2$ SUSY gauge theory from the $A_{n-1}$ quiver matrix model

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