## Classification of two-dimensional local conformal nets with c < 1 and 2-cohomology vanishing for tensor categories (2004)

Venue: | Commun. Math. Phys |

Citations: | 17 - 9 self |

### BibTeX

@ARTICLE{Kawahigashi04classificationof,

author = {Yasuyuki Kawahigashi and Roberto Longo},

title = {Classification of two-dimensional local conformal nets with c < 1 and 2-cohomology vanishing for tensor categories},

journal = {Commun. Math. Phys},

year = {2004},

volume = {244},

pages = {63--97}

}

### OpenURL

### 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 D2n+1 and E7 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 µ-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.