Strong additivity and conformal nets

Feng Xu

Vol. 221 (2005), No. 1, 167–199

DOI: 10.2140/pjm.2005.221.167

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.

Keywords

subfactor, conformal net, strong additivity

Mathematical Subject Classification 2000

Primary: 46S99, 81R10

Milestones

Received: 22 April 2003

Revised: 3 October 2004

Accepted: 18 May 2004

Published: 1 September 2005