Observables and Microscopic Entropy of Higher Spin Black Holes

Geoffrey Compère Harvard University Juan I. Jottar University Libre de Bruxelles Wei Song Tsinghua University

Mathematical Physics mathscidoc:1702.22022

Journal of High Energy Physics, 54, 2013.11
In the context of recently proposed holographic dualities between higher spin theories in AdS3 and 1+1-dimensional CFTs with W-symmetry algebras, we revisit the definition of higher spin black hole thermodynamics and the dictionary between bulk fields and dual CFT operators. We build a canonical formalism based on three ingredients: a gauge-invariant definition of conserved charges and chemical potentials in the presence of higher spin black holes, a canonical definition of entropy in the bulk, and a bulk-to-boundary dictionary aligned with the asymptotic symmetry algebra. We show that our canonical formalism shares the same formal structure as the so-called holomorphic formalism, but differs in the definition of charges and chemical potentials and in the bulk-to-boundary dictionary. Most importantly, we show that it admits a consistent CFT interpretation. We discuss the spin-2 and spin-3 cases in detail and generalize our construction to theories based on the hs[\lambda] algebra, and on the sl(N,R) algebra for any choice of sl(2,R) embedding.
AdS-CFT CorrespondenceConformal and W SymmetryBlack Holes
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  title={Observables and Microscopic Entropy of Higher Spin Black Holes },
  author={Geoffrey Compère, Juan I. Jottar, and Wei Song},
  booktitle={Journal of High Energy Physics},
Geoffrey Compère, Juan I. Jottar, and Wei Song. Observables and Microscopic Entropy of Higher Spin Black Holes . 2013. Vol. 54. In Journal of High Energy Physics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170228090716856796546.
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