Physical states and BRST operators for higher-spin W strings

In this paper, we mainly investigate the W _2,s ^M ⊗ W _2,s ^L system, in which the matter and the Liouville subsystems generate the W _2,s ^M and W _2,s ^L algebras, respectively. We first give a brief discussion of the physical states for the corresponding W strings. The lower states are given by freezing the spin-2 and spin-s currents. Then, introducing two pairs of ghost-like fields, we give the realizations of the W _1,2,s algebras. Based on these linear realizations, the BRST operators for the W _2,s algebras are obtained. Finally, we construct new BRST charges of the Liouville system for the W _2,s ^L strings at the specific values of the central charges c: for the W _2,3^L algebra, c=−24 for the W _2,4^L algebra and for the W _2,6^L algebra, at which the corresponding W _2,s ^L algebras are singular.