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Zbl 0766.46045
Boivin, Luc; Saint-Aubin, Yvan
The exchange algebra for Zamolodchikov and Fateev's parafermionic theories. (English)
[J] J. Phys. A, Math. Gen. 24, No.16, 3895-3905 (1991). ISSN 0305-4470

The author's abstract: The concept of an exchange algebra has recently been introduced by Rehren and Schroer in the context of two-dimensional conformal field theories to give an algebraic setting to both the dynamics and the locality requirement. Labelling the conformal families with two indices and assuming an interpolating scheme for one of the fields, it is shown that the braiding matrices for a subset of fields in Zamolodchikov's and Fateev's $(ZF)$ parafermionic theories containing all the order parameters are identical to those of the diagonal minimal models. We recover the full spectrum of these theories modulo integers from the phase condition of the exchange algebra even though the subset does not include the parafermionic currents.
[W.Slowikowski (Aarhus)]

MSC 2000:: *46N50 Appl. of functional analysis in quantum physics
81T40 Two-dimensional field theories, etc.

Keywords: exchange algebra; two-dimensional conformal field theories; dynamics; locality; braiding matrices; parafermionic theories; diagonal minimal models; parafermionic currents

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