In our recent publications, the partition function of the Gross–Witten–Wadia unitary matrix model with the logarithmic term has been identified with the [Formula: see text] function of a certain Painlevé system, and the double scaling limit of the associated discrete Painlevé equation to the critical point provides us with the Painlevé II equation. This limit captures the critical behavior of the [Formula: see text], [Formula: see text], [Formula: see text] supersymmetric gauge theory around its Argyres–Douglas 4D superconformal point. Here, we consider further extension of the model that contains the [Formula: see text]th multicritical point and that is to be identified with [Formula: see text] theory. In the [Formula: see text] 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.

中文翻译：

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用Argyres-Douglas点识别的具有对数势的酉矩阵模型的多临界点

在我们最近的出版物中，Gross-Witten-Wadia 酉矩阵模型与对数项的配分函数已被确定为某个 Painlevé 系统的 [公式：见文本] 函数，以及相关离散 Painlevé 的双重缩放限制到临界点的方程为我们提供了 Painlevé II 方程。此限制捕获了 [公式：见文本]、[公式：见文本]、[公式：见文本] 超对称规范理论围绕其 Argyres-Douglas 4D 超共形点的临界行为。在这里，我们考虑进一步扩展包含第 [公式：见文本] 多临界点的模型，并将其与 [公式：见文本] 理论确定。在 [公式：见文本] 的情况下，我们推导出一个由两个 ODE 组成的系统，用于自由能的标度函数，