Correlation functions of the KdV hierarchy and applications to intersection numbers over $\overline{\mathcal M}_{g,n}$

TL;DR

This paper derives explicit generating functions for correlation functions of the KdV hierarchy, providing new closed-form formulas for intersection numbers of psi- and kappa-classes on moduli spaces of curves.

Contribution

It introduces a novel explicit generating function framework for KdV tau-functions, enabling new closed-form expressions for intersection numbers on moduli spaces.

Findings

Explicit generating functions for KdV correlation functions

Closed formulas for intersection numbers of psi- and kappa-classes

Applications to full genus intersection theory

Abstract

We derive an explicit generating function of correlations functions of an arbitrary tau-function of the KdV hierarchy. In particular applications, our formulation gives closed formul\ae\ of a new type for the generating series of intersection numbers of $\psi$-classes as well as of mixed $\psi$- and $\kappa$-classes in full genera.