KP hierarchy for Hodge integrals

TL;DR

This paper derives new equations for Hodge integrals from the ELSV formula, showing that their generating functions satisfy the KP hierarchy, thus unifying and simplifying known results in the field.

Contribution

It introduces a new uniform approach to Hodge integrals by linking them to the KP hierarchy through derived equations from the ELSV formula.

Findings

Generated equations unify known results like Witten's conjecture and Virasoro constraints.

Proved that a specific generating function for Hodge integrals satisfies the KP hierarchy.

Simplified the understanding of relations among Hodge integrals.

Abstract

Starting from the ELSV formula, we derive a number of new equations on the generating functions for Hodge integrals over the moduli space of complex curves. This gives a new simple and uniform treatment of certain known results on Hodge integrals like Witten's conjecture, Virasoro constrains, Faber's lambda_g conjecture etc. Among other results we show that a properly arranged generating function for Hodge integrals satisfies the equations of the KP hierarchy.