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Homotopy algebras inspired by classical open-closed string field theory

Hiroshige Kajiura·Jim Stasheff
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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).

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BibTeXRIS

Hiroshige Kajiura, Jim Stasheff. 2006-06-30. Homotopy algebras inspired by classical open-closed string field theory. https://doi.org/10.1007/s00220-006-1539-2

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