Local Nature of Coset Models

TL;DR

This paper investigates the local structure of coset models in conformal field theory, establishing their algebraic properties, constructing holographic images, and clarifying their relation to tensor product subfactors, with applications to current subalgebras.

Contribution

It provides a detailed analysis of the local algebras of coset models, constructs conformally covariant holographic images, and clarifies their relation to tensor product subfactors, advancing the understanding of conformal subtheories.

Findings

Local algebras of coset models coincide with local relative commutants under certain conditions.

The adjoint action defines net-endomorphisms used to construct holographic images.

Applications to current subalgebras and clarification of relations to tensor product subfactors.

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.