Spectrum generating algebra and no-ghost theorem for fermionic massive string

The covariant operator quantization of the ordinary free spinning BDH string modified by adding the supersymmetric Liouville sector is analysed in the even target space dimensions d = 2, 4, 6, 8. The spectrum generating algebra for this model is constructed and a general version of the no-ghost theorem is proven. The counterpart of the GSO projection leads to a family of tachyon-free unitary free string theories. One of these models is equivalent to the non-critical Ramond-Neveu-Schwarz spinning string truncated in the Neveu-Schwarz sector to the tachyon-free eigenspace of the fermion parity operator