Flat F-manifolds, F-CohFTs, and integrable hierarchies
| Autor: | Paolo Lorenzoni, Paolo Rossi, Alessandro Arsie, Alexandr Buryak |
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| Přispěvatelé: | Arsie, A, Buryak, A, Lorenzoni, P, Rossi, P |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
F-manifold Integrable system Ramification (botany) 010102 general mathematics Integrable hierarchie FOS: Physical sciences Statistical and Nonlinear Physics Mathematical Physics (math-ph) Rank (differential topology) Type (model theory) 01 natural sciences Mathematics - Algebraic Geometry Genus (mathematics) 0103 physical sciences FOS: Mathematics Order (group theory) Field theory (psychology) 010307 mathematical physics 0101 mathematics Dispersion (water waves) Algebraic Geometry (math.AG) Mathematical Physics Mathematics |
| Popis: | We define the double ramification hierarchy associated to an F-cohomological field theory and use this construction to prove that the principal hierarchy of any semisimple (homogeneous) flat F-manifold possesses a (homogeneous) integrable dispersive deformation at all orders in the dispersion parameter. The proof is based on the reconstruction of an F-CohFT starting from a semisimple flat F-manifold and additional data in genus $1$, obtained in our previous work. Our construction of these dispersive deformations is quite explicit and we compute several examples. In particular, we provide a complete classification of rank $1$ hierarchies of DR type at the order $9$ approximation in the dispersion parameter and of homogeneous DR hierarchies associated with all $2$-dimensional homogeneous flat F-manifolds at genus $1$ approximation. 34 pages |
| Databáze: | OpenAIRE |
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