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Open-closed homotopy algebra in mathematical physics

Hiroshige Kajiura·Jim Stasheff
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Abstract

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 ($A_\infty$-algebras) by closed strings ($L_\infty$-algebras).

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Hiroshige Kajiura, Jim Stasheff. 2006-06-30. Open-closed homotopy algebra in mathematical physics. https://doi.org/10.1063/1.2171524

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