The bihamiltonian structures of the DR/DZ hierarchies at the approximation up to genus one

Abstract

In a recent paper, giving an arbitrary homogeneous cohomological field theory (CohFT), Rossi, Shadrin, and the first author proposed a simple formula for a bracket on the space local functionals that conjecturally gives a second Hamiltonian structure for the double ramification hierarchy associated to the CohFT. In this paper we prove this conjecture at the approximation up to genus 1 and relate this bracket to the second Poisson bracket of the Dubrovin-Zhang hierarchy by an explicit Miura transformation.

13 pages. arXiv admin note: text overlap with arXiv:2007.00846

References in corpus (3)

• Double ramification cycles and integrable hierarchies
• Bi-Hamiltonian recursion, Liu-Pandharipande relations, and vanishing terms of the second Dubrovin-Zhang bracket
• Quantum $D_4$ Drinfeld-Sokolov hierarchy and quantum singularity theory

Cited by in corpus (1)

• Linearization of Virasoro symmetries associated with semisimple Frobenius manifolds