Noncommutative homotopy algebras associated with open strings
Noncommutative homotopy algebras associated with open strings
复制标题
与开弦相关的非交换同伦代数
DOI：
10.1142/s0129055x07002912
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
H. Kajiura
中科院分区：
文献类型：
--
作者：
H. Kajiura
讨论了$A\infty$-代数的一般性质及其在开弦理论中的应用.研究了$A\infty$-代数的循环性的性质.证明了$A\infty$-代数和循环$A\infty$-代数的分解定理，并讨论了它的各种推论，特别是将它应用于经典开弦场论，证明了在固定共形背景上的所有经典开弦场论都是循环$A\infty$-同构的.同样的结果也适用于经典的闭弦场论，其代数结构由循环$L\infty$-代数控制。
We discuss general properties of $A_\infty$-algebras and their applications to the theory of open strings. The properties of cyclicity for $A_\infty$-algebras are examined in detail. We prove the decomposition theorem, which is a stronger version of the minimal model theorem, for $A_\infty$-algebras and cyclic $A_\infty$-algebras and discuss various consequences of it. In particular it is applied to classical open string field theories and it is shown that all classical open string field theories on a fixed conformal background are cyclic $A_\infty$-isomorphic to each other. The same results hold for classical closed string field theories, whose algebraic structure is governed by cyclic $L_\infty$-algebras.