Primitive Forms, Topological LG models coupled to Gravity and Mirror Symmetry

TL;DR

This paper explores the mathematical foundations of topological Landau-Ginzburg models coupled to gravity using primitive forms, examines mirror symmetry for Calabi-Yau manifolds and CP^1, and identifies the mirror of CP^1 with a specific primitive form theory.

Contribution

It introduces a framework connecting primitive forms with topological LG models coupled to gravity and clarifies mirror symmetry relationships for specific Calabi-Yau cases.

Findings

Mirror partner of CP^1 is the primitive form theory for f=z+qz^{-1}

Provides a mathematical foundation for LG models coupled to gravity at genus 0

Establishes connections between primitive forms and mirror symmetry in Calabi-Yau contexts

Abstract

In this paper, we will describe the mathematical foundation of topological Landau-Ginzburg (LG) models coupled to gravity at genus 0 in terms of primitive forms. We also discuss the mirror symmetry for Calabi-Yau manifolds and CP^1 in our context. We will show that the mirror partner of CP^1 is the theory of primitive form associated to f=z+qz^{-1}.