CHARACTERIZING INVARIANTS FOR LOCAL EXTENSIONS OF CURRENT-ALGEBRAS

Pairs A subset of B of local quantum field theories are studied, where A is a chiral conformal quantum field theory and B is a local extensi on, either chiral or two-dimensional. The local correlation functions of fields from B have an expansion with respect to A into conformal bl ocks, which are non-local in general. Two methods of computing charact eristic invariant ratios of structure constants in these expansions ar e compared: (a) by constructing the monodromy representation of the br aid group in the space of solutions of the Knizhnik-Zamolodchikov diff erential equation, and (b) by an analysis of the local subfactors asso ciated with the extension with methods from operator algebra (Jones th eory) and algebraic quantum field theory. Both approaches apply also t o the reverse problem: the characterization and (in principle) classif ication of local extensions of a given theory.