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arXiv · hep-th/9509119

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

Peter Bouwknegt·Jim McCarthy·Krzysztof Pilch
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Abstract

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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Peter Bouwknegt, Jim McCarthy, Krzysztof Pilch. 1995-09-22. The W_3 algebra: modules, semi-infinite cohomology and BV-algebras. https://doi.org/10.1007/978-3-540-68719-1

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