From Calabi-Yau dg Categories to Frobenius manifolds via Primitive Forms

TL;DR

This paper proposes a method to construct Frobenius manifolds from Calabi-Yau dg categories using primitive forms, advancing the understanding of mirror symmetry and categorical structures.

Contribution

It introduces a new approach to derive Frobenius manifolds from Calabi-Yau dg categories via primitive forms under formality assumptions.

Findings

Construction of formal primitive forms for Calabi-Yau dg algebras

Establishment of formal Frobenius manifolds from primitive forms

Advancement in categorical mirror symmetry theory

Abstract

It is one of the most important problems in mirror symmetry to obtain functorially Frobenius manifolds from smooth compact Calabi-Yau $A_\infty$-categories. This paper gives an approach to this problem based on the theory of primitive forms. Under an assumption on the formality of a certain homotopy algebra, a formal primitive form for a smooth compact Calabi-Yau dg algebra can be constructed, which enable us to have a formal Frobenius manifold.