Localized Endomorphisms of the Chiral Ising Model

Abstract

Based on the treatment of the chiral Ising model by Mack and Schomerus, we present examples of localized endomorphisms ${\varrho }_1^{\mathrm{loc}}$ and ${\varrho }_{1/2}^{\mathrm{loc}}$. It is shown that they lead to the same superselection sectors as the global ones in the sense that unitary equivalence ${\pi }_0\circ {\varrho }_1^{\mathrm{loc}}\cong {\pi }_1$ and ${\pi }_0\circ {\varrho }_{1/2}^{\mathrm{loc}}\cong {\pi }_{1/2}$ holds. Araki's formalism of the selfdual CAR algebra is used for the proof. We prove local normality and extend representations and localized endomorphisms to a global algebra of observables which is generated by local von Neumann algebras on the punctured circle. In this framework, we manifestly prove fusion rules and derive statistics operators.

41 pages, latex2e

References in corpus (1)

• Modular Structure and Duality in Conformal Quantum Field Theory

Cited by in corpus (8)

• Thermal States in Conformal QFT. II
• N=2 superconformal nets
• Fusion rules of modular invariants
• On Soliton Automorphisms in Massive and Conformal Theories
• Super-KMS functionals for graded-local conformal nets
• From vertex operator superalgebras to graded-local conformal nets and back
• Loop groups and noncommutative geometry
• The Charge Quantum Numbers of Gauge Invariant Quasi-free Endomorphisms