Physical states and BRST operators for higher-spin W strings

In this paper, we mainly investigate the W-2, s(M) circle times 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,W-2,W-s algebras. Based on these linear realizations, the BRST operators for the W2, 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: c=-22/5 for the W-2,3(L) algebra, c=-24 for the W-2,4(L) algebra and c= -2, -286/3 for the W-2,6(L) algebra, at which the corresponding W-2, s(L) algebras are singular.