W-strings from affine Lie algebras

The most disappointing aspect of W-strings is probably the fact that at least for the known models one does not revover a physical spectrum that differs much from that of ordinary string theory. It is hoped that this is not an intrinsic shortcoming or 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 sl₃ currents which computes the physical spectrum of a W₃-string. As a special case of this construction, if we take a free-field realization of sl₃, we recover the 2-scalar W₃-string. These results generalize to any W-algebra which can be obtained via quantum Drinfel'd-Sokolov reduction from an affine Lie algebra.