W-Strings from Affine Lie Algebras
J.M. Figueroa-O'Farrill

TL;DR
This paper introduces a new class of $ ext{W}$-strings derived from affine Lie algebra representations using quantum Drinfel'd-Sokolov reduction, leading to explicit constructions of $ ext{W}_3$-string spectra.
Contribution
It presents a novel method to construct $ ext{W}$-strings from affine Lie algebras, including explicit BRST operators and spectrum calculations for $ ext{W}_3$-strings.
Findings
Constructed a BRST operator for $ ext{W}_3$-string using $ ext{sl}_3$ currents.
Reproduced known $ ext{W}_3$-string spectra with free-field realization.
Generalized the construction to any $ ext{W}$-algebra from affine algebras.
Abstract
The most disappointing aspect of -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 -string theory, but rather that it is a consequence of the -algebra realizations that have been chosen. In this note we point out a whole new class of possible -strings built from representations of affine Lie algebras via (quantum) Drinfel'd-Sokolov reduction. Explicitly, we construct a BRST operator in terms of currents which computes the physical spectrum of a -string. As a special case of this construction, if we take a free-field realization of , we recover the 2-scalar -string. These results generalize to any -algebra which can be obtained via quantum Drinfel'd-Sokolov…
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