Abstract
Nilpotent BRST operators for higher-spin strings, with currents of spins 2 and s, have recently been constructed for s=4, 5 and 6. In the case of , this operator can be understood as being the BRST operator for the critical string. In this paper, we construct a generalized BRST operator that can be associated with a non-critical string, in which matter is coupled to the gravity of the critical case. We also obtain the complete cohomology of the critical BRST operator, and investigate the physical spectra of the s=5 and s=6 string theories.
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