Perturbation of multi-critical unitary matrix models, double scaling limits, and Argyres-Douglas theories
Perturbation of multi-critical unitary matrix models, double scaling limits, and Argyres-Douglas theories
复制标题
多临界酉矩阵模型、双标度极限和 Argyres-Douglas 理论的扰动
DOI：
10.1016/j.nuclphysb.2022.115718
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发表时间：
2021
影响因子：
2.8
通讯作者：
T. Oota
中科院分区：
文献类型：
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作者：
T. Oota
利用鞍点法，给出了一元矩阵模型的平面自由能和威尔逊环的显式形式。通过对平面自由能的研究，证明了多临界酉矩阵模型在两点处经历了三阶相变。其中一个未闭合/间隙相变是多临界的，而另一个不是多临界的。第k个多临界矩阵模型的谱曲线在多临界点处呈现4a k−1奇点。研究了多临界点周围的微扰及其双标度极限。为了达到双标度极限，应对扰动耦合常数进行微调，使光谱曲线的所有零点都接近a4k−1奇点。研究了单切状态下的微调，确定了摄动耦合的标度行为。结果表明，光谱曲线的双标度极限与Argyres-Douglas理论（A 1, A 4 k−1）的Seiberg-Witten曲线同构。
Using the saddle point method, we give an explicit form of the planar free energy and Wilson loops of unitary matrix models in the one-cut regime. The multi-critical unitary matrix models are shown to undergo third-order phase transitions at two points by studying the planar free energy. One of these ungapped/gapped phase transitions is multi-critical, while the other is not multi-critical. The spectral curve of the k-th multi-critical matrix model exhibits an A 4 k− 1 singularity at the multi-critical point. Perturbation around the multi-critical point and its double scaling limit are studied. In order to take the double scaling limit, the perturbed coupling constants should be fine-tuned such that all the zero points of the spectral curve approach to the A 4 k− 1 singular point. The fine-tuning is examined in the one-cut regime, and the scaling behavior of the perturbed couplings is determined. It is shown that the double scaling limit of the spectral curve is isomorphic to the Seiberg-Witten curve of the Argyres-Douglas theory of type (A 1, A 4 k− 1).