Homotopy algebras inspired by classical open-closed string field theory

Details Homotopy algebras inspired by classical open-closed string field theory Homotopy algebras inspired by classical open-closed string field theory

2004-10-12

arxiv.org/abs/math/0410291v3

Commun.Math.Phys. 263 (2006) 553-581

Mathematics

Quantum Algebra

30 pages, 14 figures; v2: added an appendix by M.Markl, ambiguous terminology fixed, minor corrections; v3: published version

Scientific paper

10.1007/s00220-006-1539-2

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).

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