# How to add a boundary condition

May 17, 2012

Given a conformal QFT local net of von Neumann algebras B_2 on the
two-dimensional Minkowski spacetime with irreducible subnet A\otimes\A, where A
is a completely rational net on the left/right light-ray, we show how to
consistently add a boundary to B_2: we provide a procedure to construct a
Boundary CFT net B of von Neumann algebras on the half-plane x>0, associated
with A, and locally isomorphic to B_2. All such locally isomorphic Boundary CFT
nets arise in this way. There are only finitely many locally isomorphic
Boundary CFT nets and we get them all together. In essence, we show how to
directly redefine the C* representation of the restriction of B_2 to the
half-plane by means of subfactors and local conformal nets of von Neumann
algebras on S^1.

Keywords:

*none*