On the explicit asymptotic W-5 symmetry of 3D Chern-Simons higher spin AdS(3) gravity

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Özer H. T., Filiz A.

JOURNAL OF MATHEMATICAL PHYSICS, vol.59, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 59
  • Publication Date: 2018
  • Doi Number: 10.1063/1.5042080
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Istanbul Technical University Affiliated: Yes


In this paper, we explicitly construct an asymptotic W-5 symmetry algebra of the three-dimensional anti-de Sitter (AdS(3)) higher spin gravity. We use an sl(5, R) circle plus sl (5, R) Lie algebra valued Chern-Simons gauge theory with a negative cosmological constant, and its asymptotic symmetry algebra is explicitly calculated as two copies of the classical W-5 algebra with central charge c. Our results can be interpreted as a spin 5 extension of AdS(3) gravity and a proof of how the higher spin Ward identities and the asymptotic W-5 symmetry algebra is derived from the higher spin bulk field equations of motion. This higher spin asymptotic W-5 symmetry algebra contains a finite number of conformal primary spin s: s = 2, 3, 4, 5. We also indicated how to introduce chemical potentials and holonomy conditions associated with these higher spin charges in AdS(3) higher spin gravity in a manner that it preserves the asymptotic symmetry algebra. Published by AIP Publishing.