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Physical states and BRST operators for higher-spin W strings

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Abstract

In this paper, we mainly investigate the W M2,s ⊗ W L2,s system, in which the matter and the Liouville subsystems generate the W M2,s and W L2,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 L2,s strings at the specific values of the central charges c: \(c=-\frac{22}{5}\) for the W L2,3 algebra, c=−24 for the W L2,4 algebra and \(c=-2,-\frac{286}{3}\) for the W L2,6 algebra, at which the corresponding W L2,s algebras are singular.

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Authors and Affiliations

  1. Institute of Theoretical Physics, Lanzhou University, Lanzhou, 730000, China

    Yu-Xiao Liu, Shao-Wen Wei & Ji-Rong Ren

  2. Department of Physics, Shanghai University, Shanghai, 200444, China

    Li-Jie Zhang

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  1. Yu-Xiao Liu
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  2. Shao-Wen Wei
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Correspondence to Shao-Wen Wei.

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Liu, YX., Wei, SW., Zhang, LJ. et al. Physical states and BRST operators for higher-spin W strings. Eur. Phys. J. C 60, 675–684 (2009). https://doi.org/10.1140/epjc/s10052-009-0958-6

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