Cut-and-join operators for higher Weil–Petersson volumes

Abstract

In this paper, we construct the cut-and-join operator description for the generating functions of all intersection numbers of (Formula presented.), (Formula presented.), and (Formula presented.) classes on the moduli spaces (Formula presented.). The cut-and-join operators define an algebraic version of topological recursion. This recursion allows us to compute all these intersection numbers recursively. For the specific values of parameters, the generating functions describe the volumes of moduli spaces of (super) hyperbolic Riemann surfaces with geodesic boundaries, which are also related to the Jackiw–Teitelboim (JT) (super)gravity. © 2023 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.