W-Strings from Affine Lie Algebras

Abstract

The most disappointing aspect of $\W$-strings is probably the fact that at least for the known models one does not recover a physical spectrum that differs much from that of ordinary string theory. It is hoped that this is not an intrinsic shortcoming of $\W$-string theory, but rather that it is a consequence of the $\W$-algebra realizations that have been chosen. In this note we point out a whole new class of possible $\W$-strings built from representations of affine Lie algebras via (quantum) Drinfel'd-Sokolov reduction. Explicitly, we construct a BRST operator in terms of ${\widehat{sl}}_3$ currents which computes the physical spectrum of a $\W_3$-string. As a special case of this construction, if we take a free-field realization of ${\widehat{sl}}_3$, we recover the 2-scalar $\W_3$-string. These results generalize to any $\W$-algebra which can be obtained via quantum Drinfel'd-Sokolov reduction from an affine algebra.

12 document pages (6 physical pages), uuencoded compressed .dvi file (uses AmsFonts eu* msa* msb*), QMW-PH-93-33

References in corpus (2)

• The Relation between Quantum W algebras and Lie algebras
• W3 Constructions on Affine Lie Algebras