Local Nature of Coset Models

The local algebras of the maximal Coset model C_max associated with a chiral conformal subtheory A ⊂ B are shown to coincide with the local relative commutants of A in ℬ, provided A possesses a stress-energy tensor.

Making the same assumption, the adjoint action of the unique inner-implementing representation U^A associated with A ⊂ 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 ⊂ 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.