Graph theory, SO(n) current algebra and the Virasoro master equation

We announce an isomorphism between a set of generically irrational affine-Virasoro constructions onSO(n) and the unlabelled graphs of ordern. On the one hand, the conformal constructions are classified by the graphs, while, conversely, a group-theoretic and conformal field-theoretic identification is obtained for every graph of graph theory. High-level expansion provides a strong argument that each construction is unitary down to some finite critical level.

current algebra: SO(N)
algebra: Virasoro
algebra: affine
field theory: conformal
group theory: representation
mathematical methods: graph theory
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