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

The covariant operator quantization of the ordinary free spinning BDH strin g modified by adding the supersymmetric Liouville sector is analysed in the even target space dimensions d = 2, 4, 6, 8, The spectrum generating algeb ra for this model is constructed and a general version of the no-ghost theo rem is proven. The counterpart of the GSO projection leads to a family of t achyon-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 o perator. (C) 1999 Elsevier Science B.V, All rights reserved.