Physics LettersB 296 (1992)95-103 PHYSICS LETTERS B North-Holland A derivation of the BRST operator for non-critical W-strings

Dedicated to Professor F. Cerulus on the occasion of his 65th Birthday We derive the recently proposed BRST charge for non-critical W strings from a lagrangian approach. The basic observation is that, despite appearances, the combination of two classical "matter " and "Toda " w a systems leads to a closed modified gauge algebra, which is of the so-called soft type. Based on these observations, a novel way to construct critical Wa strings is given. 1. In t roduct ion So far, all attempts to construct critical W3 strings [ 1,2] have concentrated on the standard W3 algebra of Zamolodchikov [ 3]. The corresponding BRST charge, which plays an essential role in the determination of the physical state spectrum, was constructed some time ago by Thiery-Mieg [ 4]. This result has been generalized in ref. [ 5] to arbitrary quadratically generated non-linear algebras, while in ref. [ 6] the BRST charge was derived from a lagrangian point of view. The construction of the BRST charge involves the introduction of ghosts and antighosts for the Virasoro and the spin-3 symmetries. It turns out that nilpotency of the BRST charge requires that the matter contribution cM to the central charge be cM = 100. One therefore has to search for matter reali-zations of the W3 symmetry at this value of the central charge. The standard realization of Fateev and Zamolod-chikov [ 7] involves only two free scalars, but more would be preferred in view of string applications. In ref. [ 8], realizations involving an arbitrary number of scalars were given. The application of this multi-scalar reali