, Volume 317, Issue 3, pp 667-695,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 17 Nov 2012

Construction of Wedge-Local Nets of Observables through Longo-Witten Endomorphisms. II


In the first part, we have constructed several families of interacting wedge-local nets of von Neumann algebras. In particular, we discovered a family of models based on the endomorphisms of the U(1)-current algebra \({\mathcal{A} ^{(0)}}\) of Longo-Witten.

In this second part, we further investigate endomorphisms and interacting models. The key ingredient is the free massless fermionic net, which contains the U(1)-current net as the fixed point subnet with respect to the U(1) gauge action. Through the restriction to the subnet, we construct a new family of Longo-Witten endomorphisms on \({\mathcal{A} ^{(0)}}\) and accordingly interacting wedge-local nets in two-dimensional spacetime. The U(1)-current net admits the structure of particle numbers and the S-matrices of the models constructed here do mix the spaces with different particle numbers of the bosonic Fock space.

Communicated by Y. Kawahigashi
Supported in part by the ERC Advanced Grant 227458 OACFT “Operator Algebras and Conformal Field Theory”.
Dedicated to Roberto Longo on the occasion of his 60th birthday