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Recursion Relations for Double Ramification Hierarchies

Abstract : In this paper we study various properties of the double ramification hierarchy, an integrable hierarchy of hamiltonian PDEs introduced in Buryak (Commun Math Phys 336(3): 1085-1107, 2015) using intersection theory of the double ramification cycle in the moduli space of stable curves. In particular, we prove a recursion formula that recovers the full hierarchy starting from just one of the Hamiltonians, the one associated to the first descendant of the unit of a cohomological field theory. Moreover, we introduce analogues of the topological recursion relations and the divisor equation both for the Hamiltonian densities and for the string solution of the double ramification hierarchy. This machinery is very efficient and we apply it to various computations for the trivial and Hodge cohomological field theories, and for the r-spin Witten's classes. Moreover, we prove the Miura equivalence between the double ramification hierarchy and the Dubrovin-Zhang hierarchy for the Gromov-Witten theory of the complex projective line (extended Toda hierarchy).
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01407979
Contributeur : Imb - Université de Bourgogne <>
Soumis le : vendredi 2 décembre 2016 - 18:45:23
Dernière modification le : mardi 10 novembre 2020 - 17:14:04

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Alexandr Buryak,, Paolo Rossi. Recursion Relations for Double Ramification Hierarchies. Communications in Mathematical Physics, Springer Verlag, 2016, 342 (2), pp. 533-568. ⟨10.1007/s00220-015-2535-1⟩. ⟨hal-01407979⟩

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