Hodge-GUE correspondence and the discrete KdV equation

Abstract

We prove the conjectural relationship recently proposed in [9] between certain special cubic Hodge integrals of the Gopakumar--Mariño--Vafa type [17, 28] and GUE correlators, and the conjecture proposed in [7] that the partition function of these Hodge integrals is a tau function of the discrete KdV hierarchy.

It was added the loop equation for the special cubic Hodge free energy; simplified the proof of the Main Theorem; added Corollary 1.5. 27 pages, no figures