Classification of Two-Dimensional Local Conformal Nets with <Emphasis Type="Italic">c</Emphasis> < 1 and 2-Cohomology Vanishing for Tensor Categories |
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Authors: | Yasuyuki?Kawahigashi Email author" target="_blank">Roberto?LongoEmail author |
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Institution: | (1) Department of Mathematical Sciences, University of Tokyo, Komaba, Tokyo, 153-8914, Japan;(2) Dipartimento di Matematica Università, di Roma ![lsquo](/content/2bv9qrw5eku1u1p7/xlarge8216.gif) Tor Vergata![rsquo](/content/2bv9qrw5eku1u1p7/xlarge8217.gif) Via della Ricerca Scientifica, 1, 00133 Roma, Italy |
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Abstract: | 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 -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.Supported in part by JSPS.Supported in part by GNAMPA and MIUR. |
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