Classification of 2-dimensional conformal field theories
and 2-cohomology vanishing for tensor categories
Abstract:
This is a joint work with R. Longo.
We classify 2-dimensional local conformal nets with c less than 1.
The maximal ones are in a bijective correspondence with
the pairs of A-D-E Dynkin diagrams. In our previous
classification of 1-dimensional local conformal nets,
D_odd and E_7 did not appear, but now they do appear in
this classification.
Our new main tool is 2-cohomology vanishing for certain
tensor categories.