论文标题
平坦的F-manifolds，F-Cohft和可集成的层次结构
Flat F-manifolds, F-CohFTs, and integrable hierarchies
论文作者
论文摘要
我们定义了与F-ohomologic Field理论相关的双重分析层次结构，并使用该结构来证明任何半圣经（同质）Flat F-manifold的主要层次结构在分散参数中所有阶的（均匀）具有（均匀的）集成分散性变形。该证明是基于从半圣经平坦的F-manifold开始的F-COHFT的重建，并在我们以前的工作中获得的其他数据$ 1 $。我们对这些色散变形的构建非常明确，我们计算了几个示例。特别是，我们以$ 1 $ 1 $ DR类型的等级分类为$ 9 $ $ 9 $近似，以及与所有$ 2 $ 2 $ dimensional同义的Flat F-manifolds相关的均质DR层次结构，售价为$ 1 $ 1 $ 1美元。
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.
