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Homotopy Algebras Inspired by Classical Open-Closed String Field Theory

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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 ∞-algebras) by closed strings (L ∞-algebras).

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Authors and Affiliations

  1. Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, 606-8502, Japan

    Hiroshige Kajiura

  2. Department of Mathematics, University of Pennsylvania, Philadelphia, PA, 19104-6395, USA

    Jim Stasheff

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  1. Hiroshige Kajiura
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  2. Jim Stasheff
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Correspondence to Hiroshige Kajiura.

Additional information

Communicated by L. Takhtajan

H. K is supported by JSPS Research Fellowships for Young Scientists.

J. S. is supported in part by NSF grant FRG DMS-0139799 and US-Czech Republic grant INT-0203119.

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Kajiura, H., Stasheff, J. Homotopy Algebras Inspired by Classical Open-Closed String Field Theory. Commun. Math. Phys. 263, 553–581 (2006). https://doi.org/10.1007/s00220-006-1539-2

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