L∞ spaces and derived loop spaces

摘要

We develop further the approach to derived differential geometry introduced in Costello's work on the Witten genus (arXiv, 2011). In particular, we introduce several new examples of L∞ spaces, discuss vector bundles and shifted symplectic structures on L∞ spaces, and examine in some detail the example of derived loop spaces. This paper is background for a forthcoming paper in which we define a quantum field theory on a derived stack, building upon Costello's definition of an effective field theory (AMS Monographs, 2011).