Structure of Dubrovin-Zhang free energy functions and universal identities
Mathematical Physics
2025-05-13 v2 Algebraic Geometry
math.MP
Abstract
We prove a structural theorem relating the higher genera free energy functions of the Dubrovin-Zhang hierarchies to the Witten-Kontsevich free energy function of the Korteweg-de Vries hierarchy. As an important application, for any given genus , we construct a set of universal identities valid for the free energy functions of any Dubrovin-Zhang hierarchy. In particular, we present some techniques that can be used to derive universal identities without relying on the geometry of the moduli space of stable curves of higher genus.
Cite
@article{arxiv.2405.00276,
title = {Structure of Dubrovin-Zhang free energy functions and universal identities},
author = {Sergey Shadrin and Zhe Wang},
journal= {arXiv preprint arXiv:2405.00276},
year = {2025}
}