Journal of High Energy Physics

, 2011:113 | Cite as

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

  • A. Campoleoni
  • S. FredenhagenEmail author
  • S. Pfenninger


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.


Field Theories in Lower Dimensions Chern-Simons Theories Conformal and W Symmetry 


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© SISSA, Trieste, Italy 2011

Authors and Affiliations

  1. 1.Max-Planck-Institut für GravitationsphysikAlbert-Einstein-InstitutGolmGermany

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