Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-12-07
Phys.Lett. B325 (1994) 58-62
Physics
High Energy Physics
High Energy Physics - Theory
12 document pages (6 physical pages), uuencoded compressed .dvi file (uses AmsFonts eu* msa* msb*), QMW-PH-93-33
Scientific paper
10.1016/0370-2693(94)90071-X
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.
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