论文标题
矩阵模型的穿刺和P型旋转曲线
Punctures and p-spin curves from matrix models
论文作者
论文摘要
本文研究了矩阵模型的p-Spin曲线模量空间的交点数。这些相交数字的生成函数得出的显式积分表示显示了p Stokes域，该域被“旋转” - 组件l带有值L = -1，0,1,2，...，...，P-2。较早的研究涉及P的整数值，但是当前的形式主义使我们的研究可以将我们的研究扩展到P的半数或负值P，这些值可以描述Riemann表面上的新类型的穿刺或标记点。它们分为两个类别：Ramond（L = -1），缺乏正整数P，Neveu-Schwarz（L \ ne -1）。两种类型的相交数量都是从N-Point相关函数的积分表示中计算出的，该函数在较大的N缩放限制中。我们还考虑了随机基质形式主义的超对称扩展，以表明它自然会带来额外的对数潜力。该扩展可以处理表面上的开放边界或R和NS穿刺的混合物。
This article investigates the intersection numbers of the moduli space of p-spin curves with the help of matrix models. The explicit integral representations that are derived for the generating functions of these intersection numbers exhibit p Stokes domains, labelled by a "spin"-component l taking values l = -1, 0,1,2,...,p-2. Earlier studies concerned integer values of p, but the present formalism allows one to extend our study to half-integer or negative values of p, which turn out to describe new types of punctures or marked points on the Riemann surface. They fall into two classes : Ramond (l=-1), absent for positive integer p, and Neveu-Schwarz (l\ne -1). The intersection numbers of both types are computed from the integral representation of the n-point correlation functions in a large N scaling limit. We also consider a supersymmetric extension of the random matrix formalism to show that it leads naturally to an additional logarithmic potential. Open boundaries on the surface, or admixtures of R and NS punctures, may be handled by this extension.
