Type B Topological Matter, Kodaira-Spencer Theory, and Mirror Symmetry

TL;DR

This paper introduces a topological theory combining type B matter with Kodaira-Spencer deformation, providing a framework that links mirror symmetry to two-dimensional topological field theories through genus zero correlation functions.

Contribution

It presents a novel topological theory incorporating Kodaira-Spencer deformation, advancing the understanding of mirror symmetry in topological field theories.

Findings

Genus zero three-point functions yield Yukawa couplings.

The theory explicitly includes Kodaira-Spencer deformation.

Framework potentially unifies mirror symmetry and topological matter.

Abstract

Perturbing usual type B topological matter with vector $(0,1)$-forms we find a topological theory which contains explicitly Kodaira-Spencer deformation theory. It is shown that, in genus zero, three-point correlation functions give the Yukawa couplings for a generic point in the moduli space of complex structures. This generalization of type B topological matter seems to be the correct framework to understand mirror symmetry in terms of two-dimensional topological field theories.