Moduli Space in Homological Mirror Symmetry

TL;DR

This paper establishes a homeomorphism between the moduli space of pseudo-holomorphic curves in the A-model on a symplectic torus and a moduli space of Feynman diagrams in the B-model on an elliptic curve, linking their $A_{ abla}$ structures.

Contribution

It demonstrates a novel correspondence between the moduli spaces of the A-model and B-model in homological mirror symmetry for elliptic curves.

Findings

Homeomorphism between the moduli spaces of the two models.

Determination of the $A_{ abla}$ structures by these moduli spaces.

New insights into the geometric structures underlying mirror symmetry.

Abstract

We prove that the moduli space of the pseudo holomorphic curves in the A-model on a symplectic torus is homeomorphic to a moduli space of Feynman diagrams in the configuration space of the morphisms in the B-model on the corresponding elliptic curve. These moduli spaces determine the $A_{\infty}$ structure of the both models.