Discrete Painleve system and the double scaling limit of the matrix model for irregular conformal block and gauge theory
| Autor: | Katsuya Yano, Takeshi Oota, Hiroshi Itoyama |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Physics
High Energy Physics - Theory Nuclear and High Energy Physics 010308 nuclear & particles physics Mathematical analysis FOS: Physical sciences Conformal map Unitary matrix Partition function (mathematics) 01 natural sciences Computer Science::Digital Libraries lcsh:QC1-999 Scaling limit High Energy Physics - Theory (hep-th) Critical point (thermodynamics) 0103 physical sciences Orthogonal polynomials Gauge theory 010306 general physics Scaling lcsh:Physics |
| Zdroj: | Physics Letters B, Vol 789, Iss, Pp 605-609 (2019) Physics Letters |
| DOI: | 10.48550/arxiv.1805.05057 |
| Popis: | We study the partition function of the matrix model of finite size that realizes the irregular conformal block for the case of the ${\cal N}=2$ supersymmetric $SU(2)$ gauge theory with $N_f =2$. This model has been obtained in [arXiv:1008.1861 [hep-th]] as the massive scaling limit of the $\beta$ deformed matrix model representing the conformal block. We point out that the model for the case of $\beta =1$ can be recast into a unitary matrix model with log potential and show that it is exhibited as a discrete Painlev\'{e} system by the method of orthogonal polynomials. We derive the Painlev\'{e} 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 $0$d-$4$d 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. Comment: 12 pages; v2: references added; v3: accepted version for Physics Letters B; v4: minor corrections, published version |
| Databáze: | OpenAIRE |
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