Construction of WedgeLocal Nets of Observables through LongoWitten Endomorphisms. II
Abstract
In the first part, we have constructed several families of interacting wedgelocal nets of von Neumann algebras. In particular, we discovered a family of models based on the endomorphisms of the U(1)current algebra {{A} ^{(0)}} of LongoWitten. 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 LongoWitten endomorphisms on {{A} ^{(0)}} and accordingly interacting wedgelocal nets in twodimensional spacetime. The U(1)current net admits the structure of particle numbers and the Smatrices of the models constructed here do mix the spaces with different particle numbers of the bosonic Fock space.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 February 2013
 DOI:
 10.1007/s002200121593x
 arXiv:
 arXiv:1111.1671
 Bibcode:
 2013CMaPh.317..667B
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory;
 Mathematics  Operator Algebras;
 81T05;
 81T40;
 81U99
 EPrint:
 33 pages, 1 tikz figure. The final version is available under Open Access. CCBY