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Noncommutative homotopy algebras associated with open strings
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abstract
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.
Forward citations
Cited by 3 Pith papers
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Spacetime diffeomorphisms in closed string field theory are realized as L-infinity gauge transformations, with an explicit leading-order dictionary between metric, B-field, dilaton, and flat-vertex string fields, plus...
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