Oriented Open-Closed String Theory Revisited

TL;DR

This paper revisits oriented open-closed string field theory, detailing the algebraic structures, moduli space constructions, and symmetries involved in coupling open and closed strings within string theory.

Contribution

It provides a detailed construction of open-closed string field theory with explicit algebraic and geometric structures, extending previous work to include closed strings explicitly.

Findings

Constructed a Batalin-Vilkovisky algebra on moduli spaces of bordered Riemann surfaces.

Described vertices coupling open and closed strings explicitly.

Discussed symmetries of open string theory induced by closed strings.

Abstract

String theory on D-brane backgrounds is open-closed string theory. Given the relevance of this fact, we give details and elaborate upon our earlier construction of oriented open-closed string field theory. In order to incorporate explicitly closed strings, the classical sector of this theory is open strings with a homotopy associative A_\infty algebraic structure. We build a suitable Batalin-Vilkovisky algebra on moduli spaces of bordered Riemann surfaces, the construction of which involves a few subtleties arising from the open string punctures and cyclicity conditions. All vertices coupling open and closed strings through disks are described explicitly. Subalgebras of the algebra of surfaces with boundaries are used to discuss symmetries of classical open string theory induced by the closed string sector, and to write classical open string field theory on general closed string backgrounds. We give a preliminary analysis of the ghost-dilaton theorem.