Quantum Open-Closed Homotopy Algebra and String Field Theory

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.

36 pages, fixed typos and small clarifications added

References in corpus (4)

• The Refined Topological Vertex
• Analytical Solutions of Open String Field Theory
• Closed String Cohomology in Open String Field Theory
• Quantum A-infinity Structures for Open-Closed Topological Strings

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