On the Open-Closed B-Model

TL;DR

This paper explores the relationship between open and closed strings in the topological B-model, demonstrating how closed string couplings can be derived from open string data through algebraic structures.

Contribution

It provides an explicit isomorphism between closed string couplings and the Hochschild complex of open strings, revealing a method to derive closed strings from open string algebra.

Findings

Map induces isomorphism of Gerstenhaber algebras on cohomology

Closed string couplings can be obtained from open string algebra

Potential generalizations to other models like the A-model

Abstract

We study the coupling of the closed string to the open string in the topological B-model. These couplings can be viewed as gauge invariant observables in the open string field theory, or as deformations of the differential graded algebra describing the OSFT. This is interpreted as an intertwining map from the closed string sector to the deformation (Hochschild) complex of the open string algebra. By an explicit calculation we show that this map induces an isomorphism of Gerstenhaber algebras on the level of cohomology. Reversely, this can be used to derive the closed string from the open string. We shortly comment on generalizations to other models, such as the A-model.