Strong additivity and conformal nets
It is shown that the fixed-point subnet of a strongly additive conformal net under the action of a compact group is strongly additive. Then pairs \(\mathcal B\subset\mathcal A\) of conformal nets are considered and some results on induction of pairs known earlier for the finite index case are proven for general strongly additive pairs. This is used to classify conformal nets with central charge \(c=1\) satisfying the following spectrum condition: a degenerate representation of the Virasoro net other than the vacuum representation must appear in the vacuum representation of \(\mathcal A\) if \(\mathcal A\neq\mathcal A_{c=1}\).
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