Local Nature of Coset Models

Abstract

The local algebras of the maximal Coset model C_max associated with a chiral conformal subtheory A\subset B are shown to coincide with the local relative commutants of A in B, provided A contains a stress energy tensor. Making the same assumption, the adjoint action of the unique inner-implementing representation U^A associated with A\subset B on the local observables in B is found to define net-endomorphisms of B. This property is exploited for constructing from B a conformally covariant holographic image in 1+1 dimensions which proves useful as a geometric picture for the joint inclusion A\vee C_max \subset B. Immediate applications to the analysis of current subalgebras are given and the relation to normal canonical tensor product subfactors is clarified. A natural converse of Borchers' theorem on half-sided translations is made accessible.

33 pages, no figures; typos, minor improvements

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Cited by in corpus (8)

• From vertex operator algebras to conformal nets and back
• Conformal Field Theory, Tensor Categories and Operator Algebras
• On the uniqueness of diffeomorphism symmetry in Conformal Field Theory
• Conformal covariance and related properties of chiral QFT
• Classification of subsystems for graded-local nets with trivial superselection structure
• Quantum Operations on Conformal Nets
• Conformal Covariance Subalgebras
• Absence of stress energy tensor in CFT_2 models