Meromorphic differentials, twisted DR cycles and quantum integrable hierarchies Article Swipe

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YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2408.13806

We define twisted versions of the classical and quantum double ramification hierarchy construction based on intersection theory of the strata of meromorphic differentials in the moduli space of stable curves and $k$-twisted double ramification cycles for $k=1$, respectively, we prove their integrability and tau symmetry and study their connection. We apply the construction to the case of the trivial cohomological field theory to find it produces the KdV hierarchy, although its relation to the untwisted case is nontrivial. The key role of the KdV hierarchy in controlling the intersection theory of several natural tautological classes translates this relation into a series of remarkable identities between intersection numbers involving psi-classes, Hodge classes, Norbury's theta class and the strata of meromorphic differentials.

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Meromorphic function Integrable system Quantum Pure mathematics Mathematics Algebra over a field Physics Quantum mechanics

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2408.13806
PDF: https://arxiv.org/pdf/2408.13806
OA Status: green
Related Works: 10
OpenAlex ID: https://openalex.org/W4402701708

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DOI: https://doi.org/10.48550/arxiv.2408.13806

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Title: Meromorphic differentials, twisted DR cycles and quantum integrable hierarchies

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Language: en

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Publication year: 2024

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Publication date: 2024-08-25

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Authors: Xavier Blot, Paolo Rossi

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Landing page: https://arxiv.org/abs/2408.13806

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Concepts: Meromorphic function, Integrable system, Quantum, Pure mathematics, Mathematics, Algebra over a field, Physics, Quantum mechanics

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