The classification of non-local chiral CFT with c<1
  All non-local but relatively local irreducible extensions of Virasoro chiral CFTs with c<1 are classified. The classification, which is a prerequisite for the classification of local c<1 boundary CFTs on a two-dimensional half-space, turns out to be 1 to 1 with certain pairs of A-D-E graphs with distinguished vertices. 
Y. Kawahigashi (Tokyo U.), R. Longo (Rome U.), U. Pennig, K.-H. Rehren   (Goettingen U.)