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arXiv · 2009.04852

The ${\cal N}=4$ Higher Spin Algebra for Generic $\mu$ Parameter

Changhyun Ahn·Man Hea Kim
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Abstract

The ${\cal N}=4$ higher spin generators for general superspin $s$ in terms of oscillators in the matrix generalization of $AdS_3$ Vasiliev higher spin theory at nonzero $\mu$ (which is equivalent to the 't Hooft-like coupling constant $\lambda$) were found previously. In this paper, by computing the (anti)commutators between these ${\cal N}=4$ higher spin generators for low spins $s_1$ and $s_2$ ($s_1+s_2 \leq 11$) explicitly, we determine the complete ${\cal N}=4$ higher spin algebra for generic $\mu$. 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 $\mu \leftrightarrow (1-\mu)$ up to signs. We have checked that the above ${\cal N}=4$ higher spin algebra contains the ${\cal N}=2$ higher spin algebra, as a subalgebra, found by Fradkin and Linetsky some time ago.

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Changhyun Ahn, Man Hea Kim. 2020-09-10. The ${\cal N}=4$ Higher Spin Algebra for Generic $\mu$ Parameter. https://doi.org/10.1007/jhep02(2021)123

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