Conformal nets and strong additivity

In this talk we will explain that the fixed point net of a strongly additive net under the action of a compact group is also strongly additive generalizing previous results. What is actually proved is a stronger property for the pair of nets which is called a strongly additive pair. We explain that a key theorem about the induction of a pair of nets which was proved previously under finite index conditions can be generalized to strongly additive pair with simpler proof. This is then used to classify conformal nets with central charge 1 which satisfy a spectrum condition but are not necessarily rational.