|Location:||MSRI: Simons Auditorium|
This talk concerns the question of whether any subfactor/(category of bimodules) actually comes from a conformal field theory.
The pictures in the planar algebra approach suggest the construction of a continuum limit by letting the boundary points on a disc become dense. This very optimistic idea has had some limited success, creating, for instance, toy models where the Thompson groups play the role of diffeomorphism groups. I will discuss these toy models leading up to the most recent where one constructs a limit algebra rather than a Hilbert space. A standard decomposition of the algebra shows how one can at least obtain a continuum object with diffeomorphisms acting continuously. But this ultimately only turns the question into that of finding the right state on this algebra.