On generalized fractional superstring models and the associative division algebras

A special subset of generalized fractional superstring models extending tho se of Argyres et al is studied. This subset concerns models based on SUK(K) /U(1)(K-1) Gepner parafermions. It is shown that there exists a remarkable link between generalized fractional superstrings based on SUK(K)/U(I)K-1 We ss-Zumino-Witten theory with K = 2, 3 and 5, and the associative division a lgebras. These models have critical dimensions 10, 2 x 5 and 4 x 3, respect ively, and are in one-to-one correspondence with real, Kahler, and hyper-Ka hler target spaces. Moreover, we obtain field-theoretical realizations of c o = 4 super-W-3 and c(0) = 12 super-W-5 symmetries based on the K = 3 and 5 parafermions. It is also shown that the conformal anomaly of the parafermi on ghosts of the worldsheet fractional supersymmetry is C-paraghost = 15 - K-2.