## Abstract

In this paper, we explicitly construct an asymptotic W5 symmetry algebra of the three-dimensional anti-de Sitter (AdS_{3}) higher spin gravity. We use an sl(5,R)⊕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 W5 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 W5 symmetry algebra is derived from the higher spin bulk field equations of motion. This higher spin asymptotic W5 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.

Original language | English |
---|---|

Article number | 083504 |

Journal | Journal of Mathematical Physics |

Volume | 59 |

Issue number | 8 |

DOIs | |

Publication status | Published - 1 Aug 2018 |

### Bibliographical note

Publisher Copyright:© 2018 Author(s).

### Funding

We thank Marc Henneaux for both his encouragement and constructive discussions on the manuscript. This work was supported by the Istanbul Technical University Scientific Research Projects Department (ITU BAP, Project No. 40199).

Funders | Funder number |
---|---|

ITU BAP | 40199 |

Istanbul Technical University Scientific Research Projects Department |

## Fingerprint

Dive into the research topics of 'On the explicit asymptotic W5 symmetry of 3D Chern-Simons higher spin AdS_{3}gravity'. Together they form a unique fingerprint.