On the BRST Operator of $W$-Strings

Abstract

We discuss the conditions under which the BRST operator of a $W$-string can be written as the sum of two operators that are separately nilpotent and anticommute with each other. We illustrate our results with the example of the non-critical $W_3$-string. Furthermore, we apply our results to make a conjecture about a relationship between the spectrum of a non-critical $W_n$-string and a $W_{n-1}$-string.

12 pages, UG-2/93, UCB-PTH-93/05, LBL-33737 (equations (30) and (31) have been corrected)

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Cited by in corpus (13)

• A BRST Analysis of $W$-symmetries
• $W_3$ strings, parafermions and the Ising model
• On the Cohomology of the Noncritical $W$-string
• New Realisations of Minimal Models and the Structure of W-Strings
• Embedding of the Bosonic String into the $W_3$ String
• Parafermions, $W$ Strings and their BRST Charges
• Semi-infinite cohomology and the linkage principle for $W$-algebras
• On realizing the bosonic string as a noncritical $W_3$-string
• Spinor Field Realizations of the half-integer $W_{2,s}$ Strings
• BRST cohomology of the critical $W_4$ string
• Physical States and BRST Operators for Higher-spin $W$ Strings
• Explicit field realizations of W algebras
• A BRST charge for non-critical $\W_{2,s}$ strings