• DOI:10.1142/S0129055X0400200X
• Corpus ID: 10874930

LOCAL NATURE OF COSET MODELS

@article{Koester2003LOCALNO,
  title={LOCAL NATURE OF COSET MODELS},
  author={Soeren Koester},
  journal={Reviews in Mathematical Physics},
  year={2003},
  volume={16},
  pages={353-382}
}

• Soeren Koester
• Published 24 March 2003
• Mathematics
• Reviews in Mathematical Physics

The local algebras of the maximal Coset model ${\mathcal C}_{\max}$ associated with a chiral conformal subtheory ${\mathcal A}\subset {\mathcal B}$ are shown to coincide with the local relative commutants of ${\mathcal A}$ in ℬ, provided ${\mathcal A}$ possesses a stress-energy tensor. Making the same assumption, the adjoint action of the unique inner-implementing representation $U^{\mathcal A}$ associated with ${\mathcal A}\subset {\mathcal B}$ 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 ${\mathcal A}\vee {\mathcal C}_{\max}\subset {\mathcal B}$. 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.