Closed String Cohomology in Open String Field Theory

TL;DR

This paper demonstrates that closed string states are encoded in the cyclic cohomology of open string field theory, revealing their independence from open string backgrounds and establishing an isomorphism between closed string and cyclic cohomologies.

Contribution

It establishes a novel connection between closed string states and cyclic cohomology in open string field theory, showing their independence from background and an isomorphism between cohomologies.

Findings

Closed string states are encoded in cyclic cohomology of OSFT.

Closed string cohomology is background independent.

Closed string and cyclic cohomologies are isomorphic.

Abstract

We show that closed string states in bosonic string field theory are encoded in the cyclic cohomology of cubic open string field theory (OSFT) which, in turn, classifies the deformations of OSFT. This cohomology is then shown to be independent of the open string background. Exact elements correspond to closed string gauge transformations, generic boundary deformations of Witten's 3-vertex and infinitesimal shifts of the open string background. Finally it is argued that the closed string cohomology and the cyclic cohomology of OSFT are isomorphic to each other.