Homotopy Algebras Inspired by Classical Open-Closed String Field Theory |
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Authors: | Hiroshige Kajiura Jim Stasheff |
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Institution: | (1) Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan;(2) Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104-6395, USA |
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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).
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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