Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of Two-dimensional Local Conformal Nets with c<1 and
  2-cohomology Vanishing for Tensor Categories   We classify two-dimensional local conformal nets with parity symmetry and
central charge less than 1, up to isomorphism. The maximal ones are in a
bijective correspondence with the pairs of A-D-E Dynkin diagrams with the
difference of their Coxeter numbers equal to 1. In our previous classification
of one-dimensional local conformal nets, Dynkin diagrams D_{2n+1} and E_7 do
not appear, but now they do appear in this classification of two-dimensional
local conformal nets. Such nets are also characterized as two-dimensional local
conformal nets with mu-index equal to 1 and central charge less than 1. Our
main tool, in addition to our previous classification results for
one-dimensional nets, is 2-cohomology vanishing for certain tensor categories
related to the Virasoro tensor categories with central charge less than 1.

19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con