Characterizing Invariants for Local Extensions of Current Algebras

Abstract

Pairs $å\subset \bb$ of local quantum field theories are studied, where $\mathring{a}$ 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 $\mathring{a}$ 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.

LaTeX-file, 26 pages, no figures

References in corpus (4)

• Modular Structure and Duality in Conformal Quantum Field Theory
• Nets of Subfactors
• On Structure Constants of $sl(2)$ Theories
• Subfactors and coset models

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• Critical Phenomena, modular invariants and operator algebras
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• The origin of multiplets of chiral fields in SU(2)_k WZNW at rational level
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• Modular invariants from subfactors
• Mirror Extensions of Vertex Operator Algebras