Year: 2007
Type: article
Abstract: We discuss general properties of A ∞ -algebras and their applications to the theory of open strings. The properties of cyclicity for A ∞ -algebras are examined in detail. We prove the decomposition theorem, which is a stronger version of the minimal model theorem, for A ∞ -algebras and cyclic A ∞ -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 ∞ -isomorphic to each other. The same results hold for classical closed string field theories, whose algebraic structure is governed by cyclic L ∞ -algebras.
Source: Reviews in Mathematical Physics
Author: HIROSHIGE KAJIURA
Institutions: Kyoto University, Yukawa Institute for Theoretical Physics
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2138079263