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

Abstract

This is an expanded and updated version of a talk given at the Conference on Topics 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 much background in any of them. Closed string field theory leads to a (strong homotopy) generalization of Lie algebra, which is strongly related to the way the moduli spaces $\Cal M_{0,N+1}$ fit together as an ``operad''. The latter in turn plays an important role in the understanding of vertex operator algebras.

arXiv comment23 pages amstex (8 figures NOT included)

Cited by in corpus (14)

• The Geometry of the Master Equation and Topological Quantum Field Theory
• On operad structures of moduli spaces and string theory
• On the Open-Closed B-Model
• Topological Open Membranes
• Deformations of Closed Strings and Topological Open Membranes
• Strongly homotopy algebras of a Kähler manifold
• Putting an Edge to the Poisson Bracket
• Operadic formulation of topological vertex algebras and Gerstenhaber or Batalin-Vilkovisky algebras
• Homology of moduli spaces of curves and commutative homotopy algebras
• Infinity Algebras, Massey Products, and Deformations
• The Twisted String Vertex Algorithm Applied to the $Z_2$-Twisted Scalar String Four Vertex
• Versal Deformations of Three Dimensional Lie Algebras as L-infinity Algebras
• $L_{\infty }$-algebra of an unobstructed deformation functor
• Extensions of L_infinity algebras of two even and one odd dimension