Construction of the K=8 Fractional Superconformal Algebras

We construct the K = 8 fractional superconformal algebras. There are two such extended Virasoro algebras, one of which was constructed earlier, involving a fractional spin (equivalently, conformal dimension) 5 current. The new algebra involves two additional fractional spin currents with spin 13 5 . Both algebras are nonlocal and satisfy non-abelian braiding relations. The construction of the algebras uses the isomorphism between the Z8 parafermion theory and the tensor product of two tricritical Ising models. For the special value of the central charge c = 52 55 , corresponding to the eighth member of the unitary minimal series, the 13 5 currents of the new algebra decouple, while two spin 23 5 currents (level-2 current algebra descendants of the 13 5 currents) emerge. In addition, it is shown that the K = 8 algebra involving the spin 13 5 currents at central charge c = 12 5 is the appropriate algebra for the construction of the K = 8 (four-dimensional) fractional superstring. ⋆ [email protected], [email protected] † [email protected], [email protected]