Open-closed homotopy algebra in mathematical physics

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).

38 pages, 4 figures; v2: published version

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Cited by in corpus (15)

• Homotopy algebras inspired by classical open-closed string field theory
• Conformal Field Theory and Algebraic Structure of Gauge Theory
• Quantum Open-Closed Homotopy Algebra and String Field Theory
• Matrix Factorizations, Minimal Models and Massey Products
• The classical cosmological constant of open-closed string field theory
• OCHA and Leibniz Pairs, towards a Koszul duality
• Matrix Factorizations, D-Branes and their Deformations
• Homotopy algebra of open-closed strings
• Formality theorem for Hochschild cochains via transfer
• On the Spectral Sequence of the Swiss-cheese Operad
• Categories of holomorphic line bundles on higher dimensional noncommutative complex tori
• On open-closed extension of boundary string field theory
• Bulk deformations of open topological string theory
• Homotopy representations of extended holomorphic symmetry in holomorphic twists
• Closed string amplitudes around tachyon vacuum solution in Kaku theory