On the relation between open and closed topological strings

TL;DR

This paper explores how open string correlators can be reconstructed from closed string correlators using Hochschild cohomology in topological string theories, providing computational evidence in Landau-Ginzburg models.

Contribution

It proposes a method to derive closed string correlators from open string data via Hochschild cohomology, with explicit calculations in Landau-Ginzburg models.

Findings

Hochschild cohomology of D-brane categories computed

Partial verification of the conjecture in Landau-Ginzburg models

Framework suggests a deep link between open and closed strings

Abstract

We discuss the relation between open and closed string correlators using topological string theories as a toy model. We propose that one can reconstruct closed string correlators from the open ones by considering the Hochschild cohomology of the category of D-branes. We compute the Hochschild cohomology of the category of D-branes in topological Landau-Ginzburg models and partially verify the conjecture in this case.