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

TL;DR

This survey explores the connections between closed string field theory, strong homotopy Lie algebras, and operad actions of moduli spaces, highlighting their roles in mathematical physics and vertex operator algebras.

Contribution

It provides an accessible overview linking string field theory, homotopy Lie algebras, and operad structures, emphasizing their interplay without requiring extensive background.

Findings

Closed string field theory leads to strong homotopy Lie algebra structures.

Moduli spaces form operads that relate to vertex operator algebras.

The survey clarifies the mathematical framework connecting physics and geometry.

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.