Abstract
By making use of the hidden connection between the [ℤN] parafermionic models and the [WN]p=N+1 nonlinearly extended conformal models, we show that the parafermionic descendants of the identity define, up to null currents, a WN algebra. We discuss the essential features of this “parafermionic” WN algebra, as well as the characterization of the parafermionic primary fields as WN-invariant fields. Furthermore, we show that this WN algebra can be represented, for generic values of N, in terms of only two free bosonic fields. Such a representation turns out to interpolate between two-boson representations of the W3 and the W∞ algebra known in the literature.
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