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 \(p=\frac{1}{2}\) and \(p=\frac{3}{2}\). 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.

我们在这里报告了先前工作的扩展，在该工作中我们已经证明了矩阵模型提供了一种计算p-自旋曲线的相交数的工具。我们将进一步讨论对半整数p的扩展，并详细讨论\（p = \ frac {1} {2} \）和\（p = \ frac {3} {2} \）。在这些新情况下，人们发现了来自拉蒙德部门的贡献，而对于正整数p则不存在。对于半积分自旋，也考虑存在Virasoro约束，尤其是字符串方程。通过对数矩阵模型研究了黎曼曲面边界的贡献。超对称随机矩阵提供了对正负p混合的扩展 穿刺。