Homotopy algebras inspired by classical open-closed string field theory
Quantum Algebra
2009-11-10 v3 High Energy Physics - Theory
Algebraic Topology
Abstract
We define a homotopy algebra associated to classical open-closed strings. We call it an open-closed homotopy algebra (OCHA). It is inspired by Zwiebach's open-closed string field theory and also is related to the situation of Kontsevich's deformation quantization. We show that it is actually a homotopy invariant notion; for instance, the minimal model theorem holds. Also, we show that our open-closed homotopy algebra gives us a general scheme for deformation of open string structures (A(infinity)-algebras) by closed strings (L(infinity)-algebras).
Cite
@article{arxiv.math/0410291,
title = {Homotopy algebras inspired by classical open-closed string field theory},
author = {Hiroshige Kajiura and Jim Stasheff},
journal= {arXiv preprint arXiv:math/0410291},
year = {2009}
}
Comments
30 pages, 14 figures; v2: added an appendix by M.Markl, ambiguous terminology fixed, minor corrections; v3: published version