The Complete Cohomology of the W3 String

Abstract

We present a simple procedure for constructing the complete cohomology of the BRST operator of the two-scalar and multi-scalar $W_3$ strings. The method consists of obtaining two level--15 physical operators in the two-scalar $W_3$ string that are invertible, and that can normal order with all other physical operators. They can be used to map all physical operators into non-trivial physical operators whose momenta lie in a fundamental unit cell. By carrying out an exhaustive analysis of physical operators in this cell, the entire cohomology problem is solved.

18 pages, CTP TAMU-50/93

References in corpus (7)

• Algebraic Structures and Differential Geometry in 2D String Theory
• BRST Analysis of Physical States for 2D (Super) Gravity Coupled to (Super) Conformal Matter
• Classical A_n--W-Geometry
• Discrete States in the $W_3$ String
• The Complete Spectrum of the $W_N$ String
• The $W_3$-string spectrum
• The Interacting $W_3$ String

Cited by in corpus (13)

• The conformal gauge to the derivative gauge for worldsheet gravity
• Higher order BRST and anti-BRST operators and cohomology for compact Lie algebras
• The Multivalued Free-Field Maps of Liouville and Toda Gravities
• BRST Quantisation of the N=2 String in a Real Spacetime Structure
• W-Strings 93
• Spinor Field Realizations of Non-critical $W_{2,s}$ Strings
• Canonical BRST Quantisation of Worldsheet Gravities
• $W$ Strings and Cohomology in Parafermionic Theories
• New Spinor Field Realizations of the Non-Critical $W_3$ String
• The W_3 algebra: modules, semi-infinite cohomology and BV-algebras
• BRST cohomology of the critical $W_4$ string
• Physical States and BRST Operators for Higher-spin $W$ Strings
• Explicit field realizations of W algebras