Double ramification cycles and integrable hierarchies

Abstract

It this paper we present a new construction of a hamiltonian hierarchy associated to a cohomological field theory. We conjecture that in the semisimple case our hierarchy is related to the Dubrovin-Zhang hierarchy by a Miura transformation and check it in several examples.

Final version, 18 pages

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Cited by in corpus (29)

• Tau-structure for the Double Ramification Hierarchies
• DR/DZ equivalence conjecture and tautological relations
• Bihamiltonian Cohomologies and Integrable Hierarchies II: the Tau Structures
• Flat F-manifolds, F-CohFTs, and integrable hierarchies
• Laguerre Ensemble: Correlators, Hurwitz Numbers and Hodge Integrals
• Quadratic double ramification integrals and the noncommutative KdV hierarchy
• Integrability, Quantization and Moduli Spaces of Curves
• Towards a bihamiltonian structure for the double ramification hierarchy
• Super tau-covers of bihamiltonian integrable hierarchies
• The quantum Witten-Kontsevich series and one-part double Hurwitz numbers
• A Brief Survey of FJRW Theory
• Extended $r$-spin theory in all genera and the discrete KdV hierarchy
• Tautological relations and integrable systems
• Variational Bihamiltonian Cohomologies and Integrable Hierarchies I: Foundations
• Quantum $D_4$ Drinfeld-Sokolov hierarchy and quantum singularity theory
• A conjectural formula for $D{R}_g(a,-a){\lambda }_g$
• The master relation for polynomiality and equivalences of integrable systems
• On the spectral problem of the quantum KdV hierarchy
• Linearization of Virasoro symmetries associated with semisimple Frobenius manifolds
• Hodge-Gromov-Witten theory
• Integrable systems of finite type from F-cohomological field theories without unit
• Stable tree expressions with Omega-classes and Double Ramification cycles
• A generalization of Witten's conjecture for the Pixton class and the noncommutative KdV hierarchy
• Moduli spaces of residueless meromorphic differentials and the KP hierarchy
• Quantum KdV hierarchy and shifted symmetric functions
• Faber's socle intersection numbers via Gromov--Witten theory of elliptic curve
• The bihamiltonian structures of the DR/DZ hierarchies at the approximation up to genus one
• Integrable systems associated to open extensions of type A and D Dubrovin-Frobenius manifolds
• The quantum integrable hierarchy for the Gromov-Witten theory of elliptic curves