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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.
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 th
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
Motivated by noncommutative geometry and quantum physics, the concept of `metric operator field is introduced. Roughly speaking, a metric operator field is a vector field on a set with values in self tensor product of a bundle of C*-algebras, satisfy
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
A systematic theory of product and diagonal states is developed for tensor products of $mathbb Z_2$-graded $*$-algebras, as well as $mathbb Z_2$-graded $C^*$-algebras. As a preliminary step to achieve this goal, we provide the construction of a {it f