Strong additivity and conformal nets

TL;DR

This paper proves that fixed point subnets of strongly additive conformal nets under compact group actions are strongly additive, introduces a new notion of strong additivity for pairs of nets, and applies these results to classify certain conformal nets with central charge c=1.

Contribution

It establishes the strong additivity of fixed point subnets under group actions and generalizes key induction results to strongly additive pairs of conformal nets.

Findings

Fixed point subnets of strongly additive nets are strongly additive.

A new notion of strong additivity for pairs of nets is introduced.

Classification of non-rational conformal nets with c=1 is achieved.

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 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.