论文标题
高等属的半圣经F-manifolds
Semisimple flat F-manifolds in higher genus
论文作者
论文摘要
在本文中，我们将Frobenius歧管和同一个田地理论的志式理论推广到扁平的F-manifolds和F-ohomomologic Field理论。特别是，我们为平坦的F-manifolds定义了givental锥的概念，并将givental群体的概括为作用于它们的矩阵循环群。我们表明，这种动作是在半圣经F-manifolds上进行的。然后，我们将此动作扩展到所有属中的F-Ceromological领域理论。我们表明，鉴于一个半神经平坦的F-manifold和一个将其连接到其起源的恒定f-manifold的志式组元件，可以在所有属中构建一个f-ohfts家族，并由矢量在起源的关联代数中进行参数化，其属于其属$ 0 $ part属于给定的Flat Flat Flat Flat-manifold。如果F-Manifold平坦是均匀的，则相关的F-Cohft家族包含一个同质的F-Cohfts的亚家族。但是，与Frobenius歧管和同伴不同，这些均匀的F-COHFT可以具有不同的共形尺寸，这取决于与Flat F-Manifold相关的某个指标的性质确定的。
In this paper, we generalize the Givental theory for Frobenius manifolds and cohomological field theories to flat F-manifolds and F-cohomological field theories. In particular, we define a notion of Givental cone for flat F-manifolds, and we provide a generalization of the Givental group as a matrix loop group acting on them. We show that this action is transitive on semisimple flat F-manifolds. We then extend this action to F-cohomological field theories in all genera. We show that, given a semisimple flat F-manifold and a Givental group element connecting it to the constant flat F-manifold at its origin, one can construct a family of F-CohFTs in all genera, parameterized by a vector in the associative algebra at the origin, whose genus $0$ part is the given flat F-manifold. If the flat F-manifold is homogeneous, then the associated family of F-CohFTs contains a subfamily of homogeneous F-CohFTs. However, unlike in the case of Frobenius manifolds and CohFTs, these homogeneous F-CohFTs can have different conformal dimensions, which are determined by the properties of a certain metric associated to the flat F-manifold.
