Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological Sectors and a Dichotomy in Conformal Field Theory   Let A be a local conformal net of factors on the circle with the split
property. We provide a topological construction of soliton representations of
the tensor product of n copies of A, that restrict to true representations of
subnet inviant under cyclic permutations (cyclic orbifold). 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 the cyclic orbifold has an
irreducible representation with infinite index. This implies the following
dichotomy: if all irreducible sectors of A have a conjugate sector then either
A is completely rational or A has uncountably many different irreducible
sectors. Thus A is rational iff A is completely rational. In particular, if the
mu-index of A finite then A turns out to be strongly additive. By [KLM], if A
is rational then the tensor category of representations of A is automatically
modular, namely the braiding symmetry is non-degenerate. In interesting cases,
we compute the fusion rules of the topological solitons and show that they
determine all twisted sectors of the cyclic orbifold.

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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con