arXiv subjects

Krzysztof Pilch

Publications and source records attributed to Krzysztof Pilch.

39 records · Page 3Linked to original sources

arXiv1995

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

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. [...]

hep-th↗

arXiv1992

Semi-infinite cohomology in conformal field theory and 2d gravity

We discuss various techniques for computing the semi-infinite cohomology of highest weight modules which arise in the BRST quantization of two dimensional field theories. In particular, we concentrate on two such theories -- the $G/H$ coset models and $2d$ gravity coupled to $c\leq 1$ conformal matter. (to appear in the proceedings of the XXV Karpacz Winter School)

hep-th↗

arXiv1991

Fock space resolutions of the Virasoro highest weight modules with c<=1

We extend Felder's construction of Fock space resolutions for the Virasoro minimal models to all irreducible modules with $c\leq 1$. In particular, we provide resolutions for the representations corresponding to the boundary and exterior of the Kac table.

hep-th↗