Meromorphic differentials and twisted DR hierarchies for the Hodge CohFT

2025/08/13 by Xavier Blot, Paolo Rossi, Blot, Xavier +2 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2508.09899

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.

Citations

• Faber's socle intersection numbers via Gromov--Witten theory of elliptic curve
• Meromorphic differentials, twisted DR cycles and quantum integrable hierarchies
• Polynomiality of the double ramification cycle
• Integrals of ψ-classes on twisted double ramification cycles and spaces of differentials
• Pixton's formula and Abel-Jacobi theory on the Picard stack
• A conjectural description of the tautological ring of the moduli space of curves

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• Equivalence of quantizations of the dispersionless KdV hierarchy

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