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Conformal inclusions of chiral conformal field theories, or more generally inclusions of quantum field theories, are described in the von Neumann algebraic setting by nets of subfactors, possibly with infinite Jones index if one takes non-rational theories into account. With this situation in mind, we study in a purely subfactor theoretical context a certain class of braided discrete subfactors with an additional commutativity constraint, that we call locality, and which corresponds to the commutation relations between field operators at space-like distance in quantum field theory. Examples of subfactors of this type come from taking a minimal action of a compact group on a factor and considering the fixed point subalgebra. We show that to every irreducible local discrete subfactor $mathcal{N}subsetmathcal{M}$ of type ${I!I!I}$ there is an associated canonical compact hypergroup (an invariant for the subfactor) which acts on $mathcal{M}$ by unital completely positive (ucp) maps and which gives $mathcal{N}$ as fixed points. To show this, we establish a duality pairing between the set of all $mathcal{N}$-bimodular ucp maps on $mathcal{M}$ and a certain commutative unital $C^*$-algebra, whose spectrum we identify with the compact hypergroup. If the subfactor has depth 2, the compact hypergroup turns out to be a compact group. This rules out the occurrence of compact emph{quantum} groups acting as global gauge symmetries in local conformal field theory.
Discrete subfactors include a particular class of infinite index subfactors and all finite index ones. A discrete subfactor is called local when it is braided and it fulfills a commutativity condition motivated by the study of inclusion of Quantum Fi
A theorem is derived which (i) provides a new class of subfactors which may be interpreted as generalized asymptotic subfactors, and which (ii) ensures the existence of two-dimensional local quantum field theories associated with certain modular invariant matrices.
Weighted group algebras have been studied extensively in Abstract Harmonic Analysis where complete characterizations have been found for some important properties of weighted group algebras, namely amenability and Arens regularity. One of the general
Canonical tensor product subfactors (CTPSs) describe, among other things, the embedding of chiral observables in two-dimensional conformal quantum field theories. A new class of CTPSs is constructed some of which are associated with certain modular i
We construct analogs of the embedding of orthogonal and symplectic groups into unitary groups in the context of fusion categories. At least some of the resulting module categories also appear in boundary conformal field theory. We determine when thes