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arXiv · 2107.06076

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

Oscar Brauer·Alexandr Buryak
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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.

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Oscar Brauer, Alexandr Buryak. 2021-07-13. The bihamiltonian structures of the DR/DZ hierarchies at the approximation up to genus one. https://arxiv.org/abs/2107.06076

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