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Title: 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{sub {infinity}} algebras) by closed strings (L{sub {infinity}} algebras)

Authors:
;  [1];  [2]
  1. Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)
  2. (United States)
Publication Date:
OSTI Identifier:
20768729
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 47; Journal Issue: 2; Other Information: DOI: 10.1063/1.2171524; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; DEFORMATION; GAUGE INVARIANCE; PERTURBATION THEORY; QUANTIZATION; QUANTUM FIELD THEORY; STRING MODELS; SYMMETRY

Citation Formats

Kajiura, Hiroshige, Stasheff, Jim, and Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395. Open-closed homotopy algebra in mathematical physics. United States: N. p., 2006. Web. doi:10.1063/1.2171524.
Kajiura, Hiroshige, Stasheff, Jim, & Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395. Open-closed homotopy algebra in mathematical physics. United States. doi:10.1063/1.2171524.
Kajiura, Hiroshige, Stasheff, Jim, and Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395. Wed . "Open-closed homotopy algebra in mathematical physics". United States. doi:10.1063/1.2171524.
@article{osti_20768729,
title = {Open-closed homotopy algebra in mathematical physics},
author = {Kajiura, Hiroshige and Stasheff, Jim and Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395},
abstractNote = {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{sub {infinity}} algebras) by closed strings (L{sub {infinity}} algebras)},
doi = {10.1063/1.2171524},
journal = {Journal of Mathematical Physics},
number = 2,
volume = 47,
place = {United States},
year = {Wed Feb 15 00:00:00 EST 2006},
month = {Wed Feb 15 00:00:00 EST 2006}
}