2005/10/31 by Hiroshige Kajiura, Jim Stasheff · 1 citation
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Homotopy #Homotopy and Cohomology in Algebraic Topology #Homotopy lifting property #Non-critical string theory #Quantization (signal processing) #Quantum field theory #String (physics) #String field theory #hep-th #math.AT #math.QA #n-connected
paper · pdf · doi:10.1063/1.2171524
published as J.Math.Phys.47:023506,2006 · 38 pages, 4 figures; v2: published version
openalex publication_date 2006/02/01 · arxiv created 2006/06/30 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In this paper we discuss various aspects of open-closed homotopy algebras (OCHAs) presented in our previous paper, inspired by Zwiebach’s open-closed string field theory, but that first paper concentrated on the mathematical aspects. Here we show how an OCHA is obtained by extracting the tree part of Zwiebach’s quantum open-closed string field theory. We clarify the explicit relation of an OCHA with Kontsevich’s deformation quantization and with the B-models of homological mirror symmetry. An explicit form of the minimal model for an OCHA is given as well as its relation to the perturbative expansion of open-closed string field theory. We show that our open-closed homotopy algebra gives us a general scheme for deformation of open string structures (A∞ algebras) by closed strings (L∞ algebras).