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Physical states and BRST operators for higher-spin \(W\) strings. (English) Zbl 1189.81181

Summary: We mainly investigate the \(W^M_{2,s}\otimes W^L_{2,s}\) system, in which the matter and the Liouville subsystems generate the \(W^M_{2,s}\) and \(W^L_{2,s}\) algebras, respectively. We first give a brief discussion of the physical states for the corresponding \(W\) strings. The lower states are given by freezing the spin-2 and spin-\(s\) currents. Then, introducing two pairs of ghost-like fields, we give the realizations of the \(W_{1,2,s}\) algebras. Based on these linear realizations, the BRST operators for the \(W_{2,s}\) algebras are obtained. Finally, we construct new BRST charges of the Liouville system for the \(W^L_{2,s}\) strings at the specific values of the central charges \(c\colon c=-\frac{22}{5}\) for the \(W^L_{2,3}\) algebra, \(c=-24\) for the \(W^L_{2,4}\) algebra and \(c=-2,-\frac{286}{3}\) for the \(W^L_{2,6}\) algebra, at which the corresponding \(W^L_{2,s}\) algebras are singular..

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
81T70 Quantization in field theory; cohomological methods
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