We report here an extension of a previous work in which we have shown that matrix models provide a tool to compute the intersection numbers of p-spin curves. We discuss further an extension to half-integer p, and in more details for p=1/2 and p=3/2. In those new cases one finds contributions from the Ramond sector, which were not present for positive integer p.The existence of Virasoro constraints, in particular a string equation, is considered also for half-integral spins. The contribution of the boundary of a Riemann surface, is investigated through a logarithmic matrix model The supersymmetric random matrices provide extensions to mixed positive and negative p punctures.

中文翻译：

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来自矩阵模型的穿孔和 p-Spin 曲线

我们在这里报告了先前工作的扩展，其中我们已经表明矩阵模型提供了一种计算 p-spin 曲线的交点数的工具。我们进一步讨论了半整数 p 的扩展，更详细地讨论了 p=1/2 和 p=3/2。在那些新情况下，人们发现了来自 Ramond 扇区的贡献，这对于正整数 p 不存在。Virasoro 约束的存在，特别是一个字符串方程，也被考虑用于半积分自旋。通过对数矩阵模型研究黎曼曲面边界的贡献。超对称随机矩阵提供了对混合正负 p 穿刺的扩展。