The exchange algebra for Zamolodchikov and Fateev's parafermionic theories

Abstract

The concept of an exchange algebra has recently been introduced by Rehren and Schroer (1989) 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 (1986) parafermionic theories containing all the order parameters are identical to those of the diagonal minimal models. The authors 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.