Strong additivity and conformal nets

Details Strong additivity and conformal nets Strong additivity and conformal nets

2003-03-20

arxiv.org/abs/math/0303266v2

Mathematics

Quantum Algebra

36 pages, Amstex. Prop. 3.4 improved due to a theorem of R. Longo and J. E. Roberts as pointed out by R. Longo; Added referenc

Scientific paper

We show that the fixed point subnet of a strongly additive conformal net under the action of a compact group is strongly additive. Using the idea of the proof we define the notion of strong additivity for a pair of conformal nets and we show that a key result about the induction of the pair which we proved previously under the finite index assumption can be generalized to strongly additive pairs of conformal nets. These results are applied to classify conformal nets of central charge $c=1$ which are not necessarily rational and satisfy a spectrum condition.

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