Multicritical points of unitary matrix model with logarithmic potential identified with Argyres–Douglas points
Abstrak
In [arXiv:1805.05057 [hep-th]],[arXiv:1812.00811 [hep-th]], the partition function of the Gross-Witten-Wadia unitary matrix model with the logarithmic term has been identified with the $\tau$ function of a certain Painlev\'{e} system, and the double scaling limit of the associated discrete Painlev\'{e} equation to the critical point provides us with the Painlev\'{e} II equation. This limit captures the critical behavior of the $su(2)$, $N_f =2$ $\mathcal{N}=2$ supersymmetric gauge theory around its Argyres-Douglas $4D$ superconformal point. Here, we consider further extension of the model that contains the $k$-th multicritical point and that is to be identified with $\hat{A}_{2k, 2k}$ theory. In the $k=2$ case, we derive a system of two ODEs for the scaling functions to the free energy, the time variable being the scaled total mass and make a consistency check on the spectral curve on this matrix model.
Topik & Kata Kunci
Penulis (3)
H. Itoyama
T. Oota
K. Yano
Akses Cepat
- Tahun Terbit
- 2019
- Bahasa
- en
- Total Sitasi
- 10×
- Sumber Database
- Semantic Scholar
- DOI
- 10.1142/S0217751X20501468
- Akses
- Open Access ✓