The W_3 algebra: modules, semi-infinite cohomology and BV-algebras

Physics – High Energy Physics – High Energy Physics - Theory

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144 pages; 23 uuencoded ps figures; uses macros tables.tex, epsf and amssym.def (version 2.1 or later)

Scientific paper

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. [...]

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