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arXiv · hep-th/9409165

Characterizing Invariants for Local Extensions of Current Algebras

K. -H. Rehren·Ya. S. Stanev·I. T. Todorov
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Abstract

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

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K. -H. Rehren, Ya. S. Stanev, I. T. Todorov. 1994-09-27. Characterizing Invariants for Local Extensions of Current Algebras. https://doi.org/10.1007/bf02101529

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