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Asymptotic \( \mathcal{W} \)-symmetries in three-dimensional higher-spin gauge theories

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Abstract

We discuss how to systematically compute the asymptotic symmetry algebras of generic three-dimensional bosonic higher-spin gauge theories in backgrounds that are asymptotically AdS. We apply these techniques to a one-parameter family of higher-spin gauge theories that can be considered as large N limits of SL(N) × SL(N) Chern-Simons theories, and we provide a closed formula for the structure constants of the resulting infinite-dimensional non-linear \( \mathcal{W} \)-algebras. Along the way we provide a closed formula for the structure constants of all classical \( {\mathcal{W}_N} \) algebras. In both examples the higher-spin generators of the \( \mathcal{W} \)-algebras are Virasoro primaries. We eventually discuss how to relate our basis to a non-primary quadratic basis that was previously discussed in literature.

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  1. Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, 14476, Golm, Germany

    A. Campoleoni, S. Fredenhagen & S. Pfenninger

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  1. A. Campoleoni
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  2. S. Fredenhagen
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  3. S. Pfenninger
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Correspondence to S. Fredenhagen.

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Campoleoni, A., Fredenhagen, S. & Pfenninger, S. Asymptotic \( \mathcal{W} \)-symmetries in three-dimensional higher-spin gauge theories. J. High Energ. Phys. 2011, 113 (2011). https://doi.org/10.1007/JHEP09(2011)113

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