The \(\mathcal{N} = 4\) higher spin algebra for generic \(\mu\) parameter

DOI10.1007/JHEP02(2021)123zbMATH Open1460.83061arXiv2009.04852MaRDI QIDQ2026006

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Publication date: 17 May 2021

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Abstract: The $calN=4$ higher spin generators for general superspin $s$ in terms of oscillators in the matrix generalization of $Ad{S}_3$ 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 $calN=4$ higher spin generators for low spins $s_1$ and $s_2$ ($s_1+s_{2}leq11$) explicitly, we determine the complete $calN=4$ 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 $muleftrightarrow(1-mu)$ up to signs. We have checked that the above $calN=4$ higher spin algebra contains the $calN=2$ higher spin algebra, as a subalgebra, found by Fradkin and Linetsky some time ago.

Full work available at URL: https://arxiv.org/abs/2009.04852

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