## Abstract

The N = 4 higher spin generators for general superspin s in terms of oscillators in the matrix generalization of AdS_{3} Vasiliev higher spin theory at nonzero μ (which is equivalent to the ’t Hooft-like coupling constant λ) were found previously. In this paper, by computing the (anti)commutators between these N = 4 higher spin generators for low spins s_{1} and s_{2} (s_{1} + s_{2} ≤ 11) explicitly, we determine the complete N = 4 higher spin algebra for generic μ. The three kinds of structure constants contain the linear combination of two different generalized hypergeometric functions. These structure constants remain the same under the transformation μ ↔ (1 − μ) up to signs. We have checked that the above N = 4 higher spin algebra contains the N = 2 higher spin algebra, as a subalgebra, found by Fradkin and Linetsky some time ago.

Original language | English |
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Article number | 123 |

Journal | Journal of High Energy Physics |

Volume | 2021 |

Issue number | 2 |

DOIs | |

State | Published - Feb 2021 |

## Keywords

- AdS-CFT Correspondence
- Conformal and W Symmetry
- Higher Spin Gravity
- Higher Spin Symmetry