Towards a description of the double ramification hierarchy for Witten's r-spin class
| Autor: | Jérémy Guéré, Alexandr Buryak |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Chern class Integrable system Applied Mathematics General Mathematics Computation 010102 general mathematics Hodge bundle 01 natural sciences Moduli space Mathematics - Algebraic Geometry symbols.namesake Mathematics::Algebraic Geometry Nonlinear Sciences::Exactly Solvable and Integrable Systems 0103 physical sciences symbols 010307 mathematical physics 0101 mathematics Hamiltonian (quantum mechanics) Mathematical Physics Mathematics |
| Zdroj: | Journal de Mathématiques Pures et Appliquées. 106:837-865 |
| ISSN: | 0021-7824 |
| DOI: | 10.1016/j.matpur.2016.03.013 |
| Popis: | The double ramification hierarchy is a new integrable hierarchy of hamiltonian PDEs introduced recently by the first author. It is associated to an arbitrary given cohomological field theory. In this paper we study the double ramification hierarchy associated to the cohomological field theory formed by Witten's $r$-spin classes. Using the formula for the product of the top Chern class of the Hodge bundle with Witten's class, found by the second author, we present an effective method for a computation of the double ramification hierarchy. We do explicit computations for $r=3,4,5$ and prove that the double ramification hierarchy is Miura equivalent to the corresponding Dubrovin--Zhang hierarchy. As an application, this result together with a recent work of the first author with Paolo Rossi gives a quantization of the $r$-th Gelfand--Dickey hierarchy for $r=3,4,5$. Comment: v3: 26 pages (accepted in Journal de Math\'ematiques Pures et Appliqu\'ees) |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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