Openclosed homotopy algebra in mathematical physics
Abstract
In this paper we discuss various aspects of openclosed homotopy algebras (OCHAs) presented in our previous paper, inspired by Zwiebach's openclosed 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 openclosed string field theory. We clarify the explicit relation of an OCHA with Kontsevich's deformation quantization and with the Bmodels 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 openclosed string field theory. We show that our openclosed 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:
 Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 6068502 (Japan)
 (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 191046395. Openclosed 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 191046395. Openclosed 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 191046395. Wed .
"Openclosed homotopy algebra in mathematical physics". United States.
doi:10.1063/1.2171524.
@article{osti_20768729,
title = {Openclosed homotopy algebra in mathematical physics},
author = {Kajiura, Hiroshige and Stasheff, Jim and Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 191046395},
abstractNote = {In this paper we discuss various aspects of openclosed homotopy algebras (OCHAs) presented in our previous paper, inspired by Zwiebach's openclosed 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 openclosed string field theory. We clarify the explicit relation of an OCHA with Kontsevich's deformation quantization and with the Bmodels 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 openclosed string field theory. We show that our openclosed 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}
}

Quantum current Lie algebra as the universal algebraic structure of the symmetries of completely integrable nonlinear dynamical systems of theoretical and mathematical physics
A new and extremely important property of the algebraic structure of symmetries of nonlinear infinitedimensional integrable Hamiltonian dynamical systems is described. It is that their invariance groups are isomorphic to a unique universal Banach Lie group of currents G = l /circled dot/Diff (T/sup n/) on an ndimensional torus T/sup n/. Applications of this phenomenon to the problem of constructing general criteria of integrability of nonlinear dynamical systems of theoretical and mathematical physics are considered. 
Integrability of open spin chains with quantum algebra symmetry
In this paper, the authors prove that certain quantum spin chains with quantumalgebra symmetry are integrable. Specifically these are the quantumalgebrainvariant open chains associated with the affine Lie algebras A[sub 1][sup (1)], A[sub 2n][sup (2)], A[sub 2n [minus] 1][sup (2)], B[sub n][sup (1)], C[sub n][sup (1)], and D[sub n][sup (1)] in the fundamental representation. Conspicuously absent from this list is A[sub n][sup (1)] for n [gt] 1. This is because in order to demonstrate integrability, the authors assume that the corresponding R matrix has crossing symmetry, which is not true in the case A[sub n][sup (1)] for n [gt] 1. 
BRST operator and an open gauge algebra
The authors show that in gauge theories of a general type with an open generator gauge algebra a nilpotent BRST does not exist.