Topological Sectors and a Dichotomy in Conformal Field Theory

  title={Topological Sectors and a Dichotomy in Conformal Field Theory},
  author={Roberto Longo and Feng Xu},
Let A be a local conformal net of factors on S1 with the split property. We provide a topological construction of soliton representations of the n-fold tensor product A⊗ · · · ⊗ A, that restrict to true representations of the cyclic orbifold (A ⊗ · · · ⊗ A)Zn . We prove a quantum index theorem for our sectors relating the Jones index to a topological degree. Then A is not completely rational iff the symmetrized tensor product (A ⊗ A)flip has an irreducible representation with infinite index… CONTINUE READING
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