We show that there exists a simple generalization of Kazakov's multicritical one-matrix model, which interpolates between the various multicritical points of the model. The associated multicritical potential takes the form of a power series with a heavy tail, leading to a cut of the potential and its derivative at the real axis, and reduces to a polynomial at Kazakov's multicritical points. From the combinatorial point of view the generalized model allows polygons of arbitrary large degrees (or vertices of arbitrary large degree, when considering the dual graphs), and it is the weight assigned to these large order polygons which brings about the interpolation between the multicritical points in the one-matrix model.
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 $τ$ 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 $su(2)$, $N_f =2$ $\mathcal{N}=2$ supersymmetric gauge theory around its Argyres-Douglas $4D$ superconformal point. Here, we consider further extension of the model that contains the $…
We study perturbations around the generalized Kazakov multicritical one-matrix model. The multicritical matrix model has a potential where the coefficients of $z^n$ only fall off as a power $1/n^{s+1}$. This implies that the potential and its derivatives have a cut along the real axis, leading to technical problems when one performs perturbations away from the generalized Kazakov model. Nevertheless it is possible to relate the perturbed partition function to the tau-function of a KdV hierarchy and solve the model by a genus expansion in the double scaling limit.
Non-critical String Field Theory with Non-orientable String Interactions
利用动力学三角剖分中的转移矩阵方法，研究了具有不可定向弦相互作用的非临界弦场论。对于任意的$c$（total中心荷of matter），我们构造了离散水平上的不可定向弦场论。引入了满足关系式$(\Gx)^3 = G \Gx$的两个耦合常数$G$和$\Gx$，其中$G$表示世界片的非扭曲柄数，而$\Gx$表示交叉帽数.在对应于多临界单矩阵模型的非临界弦论情形（包括$c=0$情形）中，我们成功地取了连续极限，从而得到了连续的弦场论.
