The paper proves the uniqueness part of the Hodge universality conjecture at nonzero dispersion, showing that the first Hamiltonian density determines the whole hierarchy.
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4 Pith papers cite this work, alongside 19 external citations. Polarity classification is still indexing.
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The authors define integrable observables for cohomological field theories that retain integrability, recover Dubrovin-Zhang and double ramification hierarchies, introduce a new Π-class example, prove Miura equivalences among the resulting hierarchies, and supply a short new proof of Witten's 2D-grr
Lifting a semisimple cohomological field theory by a Frobenius algebra yields non-semisimple partial CohFTs whose DR hierarchies are bi-Hamiltonian, confirming the BRS21 conjecture in these new cases.
The authors prove Dubrovin, Liu, Yang, and Zhang's conjecture: for rank-one cohomological field theories, the Dubrovin-Zhang hierarchy has a constant Poisson bracket if and only if the underlying theory is a triple Hodge class with the Calabi-Yau condition.
citing papers explorer
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A proof of the Hodge universality conjecture at nonzero dispersion
The paper proves the uniqueness part of the Hodge universality conjecture at nonzero dispersion, showing that the first Hamiltonian density determines the whole hierarchy.
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Beyond descendants: integrable observables for cohomological field theories
The authors define integrable observables for cohomological field theories that retain integrability, recover Dubrovin-Zhang and double ramification hierarchies, introduce a new Π-class example, prove Miura equivalences among the resulting hierarchies, and supply a short new proof of Witten's 2D-grr
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Lifts of partial cohomological field theories and examples of bi-Hamiltonian structures in the non-semisimple case
Lifting a semisimple cohomological field theory by a Frobenius algebra yields non-semisimple partial CohFTs whose DR hierarchies are bi-Hamiltonian, confirming the BRS21 conjecture in these new cases.
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Triple Hodge integrals and constant Poisson brackets for rank-one Dubrovin-Zhang hierarchies
The authors prove Dubrovin, Liu, Yang, and Zhang's conjecture: for rank-one cohomological field theories, the Dubrovin-Zhang hierarchy has a constant Poisson bracket if and only if the underlying theory is a triple Hodge class with the Calabi-Yau condition.