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We investigate the possibility to construct extended parafermionic conformalalgebras whose generating current has spin $1+\frac{1}{K}$, generalizing thesuperconformal (spin 3/2) and the Fateev Zamolodchikov (spin 4/3) algebras.Models invariant under such algebras would possess $Z_K$ exotic supersymmetriessatisfying (supercharge)$^K$ = (momentum). However, we show that for $K=4$ thisnew algebra allows only for models at $c=1$, for $K=5$ it is a trivialrephrasing of the ordinary $Z_5$ parafermionic model, for $K=6,7$ (and,requiring unitarity, for all larger $K$) such algebras do not exist.Implications of this result for existence of exotic supersymmetry in twodimensional field theory are discussed.Comment: 21p

ON THE POSSIBILITY OF ZN EXOTIC SUPERSYMMETRY IN TWO-DIMENSIONAL CONFORMAL FIELD THEORY

ON THE POSSIBILITY OF Z_N EXOTIC SUPERSYMMETRY IN TWO-DIMENSIONAL CONFORMAL FIELD THEORY