Karl--Henning Rehren, Yassen S. Stanev, Ivan T. Todorov
Characterizing Invariants for Local Extensions of Current Algebras
The paper is published: Commun. Math. Phys 174 (1996) 605-634

MSC:

46N50 Applications in quantum physics

81T40 Two-dimensional field theories, conformal field theories, etc.

81R10 Representations of infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody and other current algebras, See also {17B65, 17B67, 22E65, 22E67, 22E70}

46L37 Subfactors and their classification

Abstract: Pairs $\aa \subset \bb$ of local quantum field theories are studied,
where $\aa$ is a chiral conformal \qft\ and $\bb$ is a local extension,
either chiral or two-dimensional. The local correlation functions of
fields from $\bb$ have an expansion with
respect to $\aa$ into \cfb s, which are non-local in general. Two
methods of computing characteristic invariant ratios of
structure constants in these expansions are compared: $(a)$ by
constructing the monodromy \rep\ of the braid group in the space of
solutions of the Knizhnik-Zamolodchikov differential equation, and $(b)$
by an analysis of the local subfactors associated with the extension
with methods from operator algebra (Jones theory) and algebraic quantum
field theory. Both approaches apply also to the reverse problem: the
characterization and (in principle) classification of local extensions
of a given theory.

Keywords: local quantum field theories, chiral conformal quantum field theory, local extension, Knizhnik-Zamolodchikov differential equation, local subfactors