Quantum Open-Closed Homotopy Algebra and String Field Theory

TL;DR

This paper introduces the quantum open-closed homotopy algebra (QOCHA), a new algebraic framework for understanding deformations in quantum open-closed string field theory, revealing how closed string backgrounds influence open string dynamics.

Contribution

It reformulates Zwiebach's quantum open-closed string field theory using homotopy algebras, generalizing previous structures and providing new insights into deformations by closed string backgrounds.

Findings

QOCHA generalizes open-closed homotopy algebra (OCHA)

Deformations by Maurer-Cartan elements lead to consistent quantum open string theories

Homotopy formulation offers new insights into string field theory deformations

Abstract

We reformulate the algebraic structure of Zwiebach's quantum open-closed string field theory in terms of homotopy algebras. We call it the quantum open-closed homotopy algebra (QOCHA) which is the generalization of the open-closed homotopy algebra (OCHA) of Kajiura and Stasheff. The homotopy formulation reveals new insights about deformations of open string field theory by closed string backgrounds. In particular, deformations by Maurer Cartan elements of the quantum closed homotopy algebra define consistent quantum open string field theories.