BRST cohomology of the critical $W_4$ string

Abstract

We study the cohomology of the critical $W_4$ string using the $W_4$ BRST charge in a special basis in which it contains three separately nilpotent BRST charges. This allows us to obtain the physical operators in three steps. In the first step we obtain the cohomology associated to a spin-four constraint only, and it contains operators of the $c=\frac{4}{5}$ $W_3$ minimal model. In the next step, where the spin-three constraint is added, these operators get dressed to operators of the $c=\frac{7}{10}$ Virasoro minimal model. Finally, the Virasoro constraint is added to obtain the cohomology of the critical $W_4$ string. We describe the structure of the complete cohomology and compare with other results.

29 pages, LaTeX, UG-1/94

References in corpus (17)

• W-symmetry in Conformal Field Theory
• Extended N=2 Superconformal Structure of Gravity and W-Gravity Coupled to Matter
• A BRST Operator for non-critical W-Strings
• On the Spectrum and Scattering of W_3 Strings
• The Complete Spectrum of the $W_N$ String
• Discrete States in the $W_3$ String
• Explicit Construction of the BRST Charge for W_4
• A BRST Analysis of $W$-symmetries
• The Interacting $W_3$ String
• On the BRST Operator of $W$-Strings
• Critical and non-critical W_{2,4} strings
• The Complete Cohomology of the W3 String
• $W_3$ string scattering
• Semi-infinite cohomology of W-algebras
• Higher-spin strings and W minimal models
• Realisations of $W_3$ Symmetry
• Semi-infinite cohomology in conformal field theory and 2d gravity

Cited by in corpus (1)

• $W$ Strings and Cohomology in Parafermionic Theories