Entanglement and extended conformal field theory

Defining entanglement in a continuum field theory is a subtle challenge, because the Hilbert space does not naively factorize into local products.   For gauge theories, the problem arises from the gauss law constraint, and it can be resolved by an extension of the Hilbert space which introduces edge modes at the entangling surface.  Recently we showed how this extension  fits inside the frame work of 2D extended topological field theory.  In this talk we attempt a generalization to 2D CFTs in which factorization is determined by the fusion rules.  Time permitting we will speculate on applications, e.g to continuum constructions of tensor networks and to entanglement in string theory