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arXiv · 2012.05332

Flat F-manifolds, F-CohFTs, and integrable hierarchies

Alessandro Arsie·Alexandr Buryak·Paolo Lorenzoni·Paolo Rossi
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Abstract

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.

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Alessandro Arsie, Alexandr Buryak, Paolo Lorenzoni, Paolo Rossi. 2020-12-09. Flat F-manifolds, F-CohFTs, and integrable hierarchies. https://doi.org/10.1007/s00220-021-04109-8

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