Local Nature of Coset Models
Abstract
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 stressenergy tensor.
Making the same assumption, the adjoint action of the unique innerimplementing representation U^{A} associated with A ⊂ B on the local observables in ℬ is found to define netendomorphisms 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 halfsided translations is made accessible.
 Publication:

Reviews in Mathematical Physics
 Pub Date:
 2004
 DOI:
 10.1142/S0129055X0400200X
 arXiv:
 arXiv:mathph/0303054
 Bibcode:
 2004RvMaP..16..353K
 Keywords:

 Conformal quantum field theory;
 nets of subfactors;
 coset construction;
 current algebras;
 isotony;
 Mathematical Physics;
 81T05;
 81T40;
 46L60
 EPrint:
 33 pages, no figures