On the BRST Operator of $W$-Strings

E. Bergshoeff, H. J. Boonstra, M. de Roo, S. Panda, A. Sevrin

Published 1993-03-09, updated 1993-03-12Version 2

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.