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Communications in Mathematical Physics

, Volume 317, Issue 3, pp 667–695 | Cite as

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

  • Marcel Bischoff
  • Yoh Tanimoto
Open Access
Article

Abstract

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.

Keywords

Gauge Action Asymptotic Completeness Conformal Character Positive Energy Representation Standard Subspace 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

We thank our supervisor Roberto Longo for his constant support and useful suggestions. Y. T. thanks Gandalf Lechner and Jan Schlemmer for discussions on the relation between the present construction and the deformation of [Lec11].

Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

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Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomaItaly
  2. 2.Institute für Theoretische PhysikUniversität GöttingenGoettingenGermany

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