The spin-$\frac{4}{3}$ fractional superstring is characterized by a world-sheet chiral algebra involving spin-$\frac{4}{3}$ currents. The discussion of the tree-level scattering amplitudes of this theory presented in the preceding paper is expanded to include amplitudes containing two twisted-sector states. These amplitudes are shown to satisfy spurious state decoupling. The restriction to only two external twisted-sector states is due to the absence of an appropriate dimension-one vertex describing the emission of a single twisted-sector state. This is analogous to the "old covariant" formalism of ordinary superstring amplitudes in which an appropriate dimension-one vertex for the emission of a Ramond-sector state is lacking. Examples of tree scattering amplitudes are calculated in a $c=5\mathrm{}$ model of the spin-$\frac{4}{3}$ chiral algebra realized in terms of free bosons on the string world sheet. The target space of this model is three-dimensional flat Minkowski space-time and the twisted-sector physical states are fermions in space-time. Since the critical central charge of the spin-4/3 fractional superstring theory is 10, this $c=5\mathrm{}$ model is not consistent at the string loop level.

• Received 22 November 1993

DOI:https://doi.org/10.1103/PhysRevD.49.5349