Meromorphic differentials and twisted DR hierarchies for the Hodge CohFT

TL;DR

This paper extends the connection between meromorphic differentials, twisted DR hierarchies, and the untwisted DR hierarchy to the Hodge CohFT, revealing new identities among Hodge integrals and DR cycles.

Contribution

It generalizes the correspondence between hierarchies to the Hodge CohFT, establishing new identities involving Hodge integrals and DR cycles.

Findings

Established a correspondence between Hodge CohFT and untwisted DR hierarchy.

Derived new identities between Hodge integrals over different cycles.

Extended the framework of integrable hierarchies to include Hodge structures.

Abstract

In [arXiv:2408.13806], two families of classical and quantum integrable hierarchies associated to arbitrary Cohomological Field Theories (CohFTs) were introduced: the meromorphic differential and twisted double ramification hierarchies. For trivial CohFT, the authors established a connection with the untwisted Double Ramification (DR) hierarchy. In this paper, we extend this study to the Hodge CohFT and prove an analogous correspondence with the untwisted DR hierarchy. This yields non-trivial identities between Hodge integrals over the DR cycle, the twisted DR cycle and the cycle of meromorphic differentials.