Quantum Cohomology And All That

TL;DR

This paper explores a novel connection between quantum cohomology in topological sigma models and the Chern-Simons theory of the quantum Hall effect, revealing an underlying isomorphism and its implications for supersymmetric and quantization structures.

Contribution

It establishes an isomorphism between quantum cohomology arising from the quantum Hall effect and that from topological sigma models, linking different theoretical frameworks.

Findings

Identified quantum cohomology as an invariant property of the quantum Hall effect

Demonstrated the equivalence between quantum cohomologies of different models

Suggested a relation between supersymmetric structures and topological theories

Abstract

We found a quantum cohomology/homology of quantum Hall effect which arises as the invariant property of the Chern-Simons theory of quantum Hall effect and showed that it should be equivalent to the quantum cohomology which arose as the invariant property of topological sigma models. This isomorphism should be related with an equivalence between the supersymmetric- and quantization structures in two dimensional models and/or with an equivalence between topological sigma models and the Chern-Simons theory by the methode of master equation.