THE WORLDSHEET CONFORMAL FIELD-THEORY OF THE FRACTIONAL SUPERSTRING

Two of the important unresolved issues concerning fractional superstri ngs have been the appearance of new massive sectors whose space-time s tatistics properties are unclear, and the appearance of new types of ' 'internal projections'' which alter or deform the worldsheet conformal field theory in a highly non-trivial manner. In this paper we provide a systematic analysis of these two connected issues, and explicitly m ap out the effective post-projection worldsheet theories for each of t he fractional-superstring sectors. In this way we determine their cent ral charges, highest weights, fusion rules, and characters, and find t hat these theories are isomorphic to those of free worldsheet bosons a nd femions. We also analyze the recently-discovered parafermionic ''tw ist current'' which has been shown to play an important role in reorga nizing the fractional-superstring Fock space, and find that this curre nt can be expressed directly in terms of the primary fields of the pos t-projection theory. This thereby enables us to deduce some of the spa ce-time statistics properties of the surviving states.