标题： 超体积和KdV tau函数 显示英文标题

标题： Super volumes and KdV tau functions

摘要： 威普体积与康采维奇-威滕KdV tau函数密切相关。 它们具有一个由米扎卡尼基于体积之间的递归关系得出的Virasoro对称性。 类似地，具有Neveu-Schwarz穿孔的超曲线模空间的超威普体积与KdV层级的Brézin-Gross-Witten (BGW) tau函数相关，并且满足斯坦福德和 威滕的递归关系，类似于米扎卡尼的递归。 在本文中，我们证明了通过允许Ramond穿孔，超威普体积与广义BGW KdV tau函数相关，后者是BGW tau函数的一个参数变形。 这使我们能够证明这些新的超体积也满足斯坦福德-威滕递归。 显示英文摘要

摘要： Weil-Petersson volumes of the moduli space of curves are deeply related to the Kontsevich-Witten KdV tau function. They possess a Virasoro symmetry which comes out of recursion relations between the volumes due to Mirzakhani. Similarly, the super Weil-Petersson volumes of the moduli space of super curves with Neveu-Schwarz punctures are related to the Br\'ezin-Gross-Witten (BGW) tau function of the KdV hierarchy and satisfy a recursion due to Stanford and Witten, analogous to Mirzakhani's recursion. In this paper we prove that by also allowing Ramond punctures, the super Weil-Petersson volumes are related to the generalised BGW KdV tau function, which is a one parameter deformation of the BGW tau function. This allows us to prove that these new super volumes also satisfy the Stanford-Witten recursion.