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Discrete Painlevé system and the double scaling limit of the matrix model for irregular conformal block and gauge theory

2018/05/31 by H. Itoyama, Hiroshi Itoyama, Takeshi Oota +1 · 20 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Conformal map #Gauge (firearms) #Gauge theory #Geometry #Limit (mathematics) #Mathematical analysis #Mathematical physics #Matrix (chemical analysis) #Matrix model #Nonlinear Waves and Solitons #Physics #Quantum Chromodynamics and Particle Interactions #Quantum electrodynamics #Scaling #Scaling limit #String (physics) #Theoretical physics #hep-th

paper · pdf · doi:10.1016/j.physletb.2018.10.077

published in Physics Letters B 789, 605-609 (Elsevier BV) · 12 pages; v2: references added; v3: accepted version for Physics Letters B; v4: minor corrections, published version

openalex publication_date 2019/01/02 · arxiv created 2019/01/03 · arxiv updated 2019/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study the partition function of the matrix model of finite size that realizes the irregular conformal block for the case of the N=2 supersymmetric SU(2) gauge theory with Nf=2. This model has been obtained in arXiv:1008.1861 [hep-th] as the massive scaling limit of the β-deformed matrix model representing the conformal block. We point out that the model for the case of β=1 can be recast into a unitary matrix model with log potential and show that it is exhibited as a discrete Painlevé system by the method of orthogonal polynomials. We derive the Painlevé II equation, taking the double scaling limit in the vicinity of the critical point which is the Argyres–Douglas type point of the corresponding spectral curve. By the 0d-4d dictionary, we obtain the time variable and the parameter of the double scaled theory respectively from the sum and the difference of the two mass parameters scaled to their critical values.

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