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

TL;DR

This paper develops a cut-and-join operator framework for computing intersection numbers on moduli spaces, linking it to topological recursion and volumes of hyperbolic Riemann surfaces relevant to JT gravity.

Contribution

It introduces a novel algebraic cut-and-join operator approach for all intersection numbers involving psi, kappa, and Theta classes, enabling recursive volume computations.

Findings

Constructed cut-and-join operators for intersection number generating functions

Established algebraic topological recursion for these functions

Connected volumes of moduli spaces to JT (super)gravity models

Abstract

In this paper, we construct the cut-and-join operator description for the generating functions of all intersection numbers of $\psi$, $\kappa$, and $\Theta$ classes on the moduli spaces $\overline{\mathcal M}_{g,n}$. 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.