Polynomial recursion formula for linear Hodge integrals

TL;DR

This paper introduces a polynomial recursion formula for linear Hodge integrals derived from Hurwitz numbers, connecting to the Witten-Kontsevich theorem and lambda_g formula, advancing the understanding of intersection theory.

Contribution

It presents a novel polynomial recursion formula for linear Hodge integrals, linking Hurwitz numbers and intersection theory in a new way.

Findings

Recovers the Witten-Kontsevich theorem in top degree terms

Derives the lambda_g formula's combinatorial factor as lowest degree terms

Establishes a new recursion relation for linear Hodge integrals

Abstract

We establish a polynomial recursion formula for linear Hodge integrals. It is obtained as the Laplace transform of the cut-and-join equation for the simple Hurwitz numbers. We show that the recursion recovers the Witten-Kontsevich theorem when restricted to the top degree terms, and also the combinatorial factor of the lambda_g formula as the lowest degree terms.