Open-closed homotopy algebra in mathematical physics

Details Open-closed homotopy algebra in mathematical physics Open-closed homotopy algebra in mathematical physics

2005-10-14

arxiv.org/abs/hep-th/0510118v2

J.Math.Phys.47:023506,2006

Physics

High Energy Physics

High Energy Physics - Theory

38 pages, 4 figures; v2: published version

Scientific paper

10.1063/1.2171524

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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