Spinor Field Realizations of Non-critical W2,sW_{2,s} Strings

In this paper, we construct the nilpotent Becchi-Rouet-Stora-Tyutin($BRST$) charges of spinor non-critical $W_{2,s}$ strings. The cases of $s=3,4$ are discussed in detail, and spinor realization for $s=4$ is given explicitly. The $BRST$ charges are graded.Comment: 9 pages, no figure

Classification of irreducible weight modules over higher rank Virasoro algebras

Let $G$ be a rank $n$ additive subgroup of \bC and \Vir[G] the corresponding Virasoro algebra of rank $n$. In the present paper, irreducible weight modules with finite dimensional weight spaces over \Vir[G] are completely determined. There are two different classes of them. One class consists of simple modules of intermediate series whose weight spaces are all 1-dimensional. The other is constructed by using intermediate series modules over a Virasoro subalgebra of rank $n-1$. The classification of such modules over the classical Virasoro algebra was obtained by O. Mathieu in 1992 using a completely different approach.Comment: 24 page