Quaternion Landau-Ginsburg models and noncommutative Frobenius manifolds

TL;DR

This paper introduces a quaternion Landau-Ginsburg model extending classical topological models, and proves its moduli space forms a non-commutative Frobenius manifold, linking topological field theory with non-commutative geometry.

Contribution

It develops a new quaternion Landau-Ginsburg model satisfying open-closed topological field theory axioms and establishes its moduli space as a non-commutative Frobenius manifold.

Findings

Quaternion Landau-Ginsburg models satisfy open-closed topological field theory axioms

Moduli space of these models forms a non-commutative Frobenius manifold

Extension of classical models to non-commutative settings

Abstract

We extend the classical topological Landau-Ginsburg model to a quaternion Landau-Ginsburg model, that satisfy the axioms of open-closed topological field theory. Later we prove, that a moduli space of quaternion Landau-Ginsburg models are non-commutative Frobenius manifold in means of [J. Geom. Phys, 51 (2003), 387-403].