Analogous to the background independent open string field theory by Witten. If there isn't, what are the main stumbling blocks preventing its construction?
By locality I mean something like the Atiyah-Segal axioms for Riemannian cobordisms (see e.g. http://ncatlab.org/nlab/show/FQFT). I.e. to any (spacelike) hypersurface in the target we associate a ...