Discrete Painleve system for the partition function of N_f =2 SU(2) supersymmetric gauge theory and its double scaling limit

2018/12/31 by Hiroshi Itoyama, Takeshi Oota, Katsuya Yano · 1 citation
Physics and Astronomy · #hep-th

paper · pdf · doi:10.1088/1751-8121/ab3f4f

61 pages, 6 figures; v2. a reference added; v3. 63 pages, published version

arxiv created 2019/10/06 · arxiv updated 2020/01/08

Abstract

We continue to study the matrix model of the N_f =2 SU(2) case that represents the irregular conformal block. What provides us with the Painlevé system is not the instanton partition function per se but rather a finite analog of its Fourier transform that can serve as a generating function. The system reduces to the extension of the Gross-Witten-Wadia unitary one-matrix model by the logarithmic potential while keeping the planar critical behavior intact. The double scaling limit to this critical point is a constructive way to study Argyres-Douglas type theory from IR. We elaborate upon the method of orthogonal polynomial and its relevance to these problems, developing it further for the case of a generic unitary matrix model and that of a special case with the logarithmic potential.

Cited by

• Multicritical points of unitary matrix model with logarithmic potential identified with Argyres-Douglas points

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