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 $\psi$, $\kappa$, 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.

arXiv comment13 pages; published version

References in corpus (8)

• JT gravity as a matrix integral
• Cut-and-Join operator representation for Kontsevich-Witten tau-function
• A new cohomology class on the moduli space of curves
• Cut-and-join description of generalized Brezin-Gross-Witten model
• JT supergravity and Brezin-Gross-Witten tau-function
• KP integrability of triple Hodge integrals. II. Generalized Kontsevich matrix model
• Recursion formulae of higher Weil-Petersson volumes
• Gromov-Witten invariants of ${\mathbb{P}}^1$ coupled to a KdV tau function

Cited by in corpus (2)

• Some Generalizations of Mirzakhani's Recursion and Masur-Veech Volumes via Topological Recursions
• Cut-and-join operators in cohomological field theory and topological recursion