1999/03/31 by Yasuyuki Kawahigashi, Roberto Longo, Michael Mueger · 3 citations
Mathematics · Physics and Astronomy · #hep-th #math-ph #math.MP #math.OA #msc:46L37 #msc:46M05 #msc:81T05
paper · pdf · doi:10.1007/pl00005565
published as Commun.Math.Phys.219:631-669,2001 · 45 pages, AMSLatex 2e. Improvements concerning the exposition. Appendices have been expanded with more details. To appear in Commun. Math. Phys
arxiv created 2001/01/15 · arxiv updated 2011/04/06
We describe the structure of the inclusions of factors A(E) contained in A(E')' associated with multi-intervals E of R for a local irreducible net A of von Neumann algebras on the real line satisfying the split property and Haag duality. In particular, if the net is conformal and the subfactor has finite index, the inclusion associated with two separated intervals is isomorphic to the Longo-Rehren inclusion, which provides a quantum double construction of the tensor category of superselection sectors of A. As a consequence, the index of A(E) in A(E')' coincides with the global index associated with all irreducible sectors, the braiding symmetry associated with all sectors is non-degenerate, namely the representations of A form a modular tensor category, and every sector is a direct sum of sectors with finite dimension. The superselection structure is generated by local data. The same results hold true if conformal invariance is replaced by strong additivity and there exists a modular PCT symmetry.