Closed string field theory, strong homotopy Lie algebras and the operad actions of moduli space

摘要

This is an expanded and updated version of a talk given at the Conference onTopics in Geometry and Physics at the University of Southern California,November 6, 1992. It is a survey talk, aimed at mathematicians AND physicists,which attempts to bring together the topics in the title without assuming muchbackground in any of them. Closed string field theory leads to a (stronghomotopy) generalization of Lie algebra, which is strongly related to the waythe moduli spaces $\Cal M_{0,N+1}$ fit together as an ``operad''. The latter inturn plays an important role in the understanding of vertex operator algebras.