\mathcal{W} symmetry and integrability of higher spin black holes

Geoffrey Compère gcompere@ulb.ac.be Wei Song Tsinghua University

Mathematical Physics mathscidoc:1702.22023

Journal of High Energy Physics, 144, 2013.9
We obtain the asymptotic symmetry algebra of Chern-Simons theory with Dirichlet boundary conditions for fixed chemical potential. These boundary conditions are obeyed by higher spin black holes. For each embedding of into , we show that the asymptotic symmetry group is independent of the chemical potential. On the one hand, starting from AdS in the principal embedding, we show that the symmetry is preserved upon turning on perturbatively spin 3 chemical potentials. On the other hand, starting from AdS in the diagonal embedding, we show that the symmetry is preserved upon turning on finite spin 3/2 chemical potentials. We also make connections between the canonical Lagrangian formalism and integrability methods based on the n = 3 KdV (Boussinesq) hierarchy.
AdS-CFT CorrespondenceConformal and W SymmetryIntegrable Equations in PhysicsIntegrable Hierarchies
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@inproceedings{geoffrey2013\mathcal{w},
  title={\mathcal{W} symmetry and integrability of higher spin black holes},
  author={Geoffrey Compère, and Wei Song},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170228091241071060547},
  booktitle={Journal of High Energy Physics},
  volume={144},
  year={2013},
}
Geoffrey Compère, and Wei Song. \mathcal{W} symmetry and integrability of higher spin black holes. 2013. Vol. 144. In Journal of High Energy Physics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170228091241071060547.
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