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
Symplectic geometry of Frobenius structures
4 Pith papers cite this work, alongside 440 external citations. Polarity classification is still indexing.
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Near a regular nodal degeneration, topological recursion is shown to factor into the normalization, a universal Gaussian vacuum, and a positive-vanishing-period graph sum, which recovers the conifold gap.
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.
For the Calabi-Yau threefolds Z6, Z8, Z10 in weighted projective space, the BCOV Feynman rule and Yamaguchi-Yau anomaly equations are proved, giving polynomial recursions for all genus Gromov-Witten invariants.
citing papers explorer
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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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Conifold factorization in topological recursion and Gromov--Witten theory
Near a regular nodal degeneration, topological recursion is shown to factor into the normalization, a universal Gaussian vacuum, and a positive-vanishing-period graph sum, which recovers the conifold gap.
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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.
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Higher genus Gromov-Witten theory of one-parameter Calabi-Yau threefolds II: Feynman rule and anomaly equations
For the Calabi-Yau threefolds Z6, Z8, Z10 in weighted projective space, the BCOV Feynman rule and Yamaguchi-Yau anomaly equations are proved, giving polynomial recursions for all genus Gromov-Witten invariants.