Conformal nets II: conformal blocks

Understand

Conformal nets provide a mathematical formalism for conformal field theory.

• Associated to a conformal net with finite index, we give a construction of the `bundle of conformal blocks', a representation of the mapping class groupoid of closed topological surfaces into the category of finite-dimensional projective Hilbert spaces.
• We also construct infinite-dimensional spaces of conformal blocks for topological surfaces with smooth boundary.
• We prove that the conformal blocks satisfy a factorization formula for gluing surfaces along circles, and an analogous formula for gluing surfaces along intervals.