Hodge-GUE correspondence and the discrete KdV equation
Mathematical Physics
2018-10-30 v2 Algebraic Geometry
math.MP
Abstract
We prove the conjectural relationship recently proposed in [9] between certain special cubic Hodge integrals of the Gopakumar--Mari\~no--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.
Keywords
Cite
@article{arxiv.1612.02333,
title = {Hodge-GUE correspondence and the discrete KdV equation},
author = {Boris Dubrovin and Si-Qi Liu and Di Yang and Youjin Zhang},
journal= {arXiv preprint arXiv:1612.02333},
year = {2018}
}
Comments
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