Discrete Painleve system for the partition function of $N_f =2$ $SU(2)$ supersymmetric gauge theory and its double scaling limit
| Autor: | Itoyama, Hiroshi, Oota, Takeshi, Yano, Katsuya |
|---|---|
| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1751-8121/ab3f4f |
| Popis: | 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 Painlev\'{e} 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. Comment: 61 pages, 6 figures; v2. a reference added; v3. 63 pages, published version |
| Databáze: | arXiv |
| Externí odkaz: |
|