Entanglement branes and factorization in conformal field theory

In this work, we consider the question of local Hilbert space factorization in 2D conformal field theory. Generalizing previous work on entanglement and open-closed TQFT, interpret CFT states terms path integral processes that split join spaces circles intervals. More abstractly, these are cobordisms an extended which defined purely OPE data. addition to usual sewing axioms, impose boundary condition is satisfied by vacuum Ishibashi state. This choice state leads reduced density matrices sum over super-selection sectors, identify as edge modes. Finally, relate our map co-product formula for symmetry algebra, show equivalent a Boguliubov transformation case free boson.