Abstract:
In a recent paper, given an arbitrary homogeneous cohomological field theory (CohFT),
Rossi, Shadrin, and the first author proposed a simple formula for a bracket on the space of
local functionals, which conjecturally gives a second Hamiltonian structure
for the double ramification hierarchy associated to the CohFT. In this paper we prove
this conjecture in the approximation up to genus 1 for any semisimple CohFT and relate this bracket
to the second Poisson bracket of the Dubrovin–Zhang hierarchy by an explicit Miura transformation.
Keywords:
moduli space of curves, cohomology ring, partial differential equation.
Citation:
O. Brauer, A. Yu. Buryak, “The Bi-Hamiltonian Structures of the DR and DZ Hierarchies in the Approximation up to Genus One”, Funktsional. Anal. i Prilozhen., 55:4 (2021), 22–39; Funct. Anal. Appl., 55:4 (2021), 272–285
\Bibitem{BraBur21}
\by O.~Brauer, A.~Yu.~Buryak
\paper The Bi-Hamiltonian Structures of the DR and DZ Hierarchies in the Approximation up to Genus One
\jour Funktsional. Anal. i Prilozhen.
\yr 2021
\vol 55
\issue 4
\pages 22--39
\mathnet{http://mi.mathnet.ru/faa3933}
\crossref{https://doi.org/10.4213/faa3933}
\transl
\jour Funct. Anal. Appl.
\yr 2021
\vol 55
\issue 4
\pages 272--285
\crossref{https://doi.org/10.1134/S001626632104002X}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000770340500002}
Linking options:
https://www.mathnet.ru/eng/faa3933
https://doi.org/10.4213/faa3933
https://www.mathnet.ru/eng/faa/v55/i4/p22
This publication is cited in the following 2 articles:
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