/sci/ - Science & Math

>>8956587
Ok.
My idea comes from the AdS/CFT correspondence, which maps cobordisms of surfaces in AdS into states in a CFT, and which maps GR surface entropy into the von Neumann entropy of states. The first part looks identical to the categorical definition of a TQFT a la Atiyah, and I'm wondering if there is some way to endow TQFTs with some kind of geometric data that's analogous to volume/surface entropy so that we can completely characterize the correspondence by making sure that the TQFT functor maps the surface entropy to a quantity that satisfy some properties of the von Neumann entropy. Then afterwards we can try to classify these special TQFTs.