Strong additivity and conformal nets

Abstract

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 fact about induction of pairs, proved earlier under the assumption of finite index, can be generalized to strongly additive pairs of conformal nets. These results are used to classify conformal nets of central charge c = 1 that are not necessarily rational and satisfy a spectrum condition.