%0 Journal Article
%T The W_3 algebra: modules, semi-infinite cohomology and BV-algebras
%A Peter Bouwknegt
%A Jim McCarthy
%A Krzysztof Pilch
%J Mathematics
%D 1995
%I arXiv
%R 10.1007/978-3-540-68719-1
%X The noncritical $D=4$ $W_3$ string is a model of $W_3$ gravity coupled to two free scalar fields. In this paper we discuss its BRST quantization in direct analogy with that of the $D=2$ (Virasoro) string. In particular, we calculate the physical spectrum as a problem in BRST cohomology. The corresponding operator cohomology forms a BV-algebra. We model this BV-algebra on that of the polyderivations of a commutative ring on six variables with a quadratic constraint, or, equivalently, on the BV-algebra of (polynomial) polyvector fields on the base affine space of $SL(3,C)$. In this paper we attempt to present a complete summary of the progress made in these studies. [...]
%U http://arxiv.org/abs/hep-th/9509119v1