Hodge-GUE correspondence and the discrete KdV equation

Dubrovin, Boris; Liu, Si-Qi; Yang, Di; Zhang, Youjin

doi:10.1007/s00220-020-03846-6

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Hodge-GUE correspondence and the discrete KdV equation

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Yang, Di
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s00220-020-03846-6
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Citation

Dubrovin, B., Liu, S.-Q., Yang, D., & Zhang, Y. (2020). Hodge-GUE correspondence and the discrete KdV equation. Communications in Mathematical Physics, 379(2), 461-490. doi:10.1007/s00220-020-03846-6.

Cite as: https://hdl.handle.net/21.11116/0000-0007-16EE-5

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.