The $$ \mathcal{N} $$ = 4 higher spin algebra for generic μ parameter

Abstract

Abstract The $$ \mathcal{N} $$ N = 4 higher spin generators for general superspin s in terms of oscillators in the matrix generalization of AdS3 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 $$ \mathcal{N} $$ N = 4 higher spin generators for low spins s1 and s2 (s1 + s2 ≤ 11) explicitly, we determine the complete $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ N = 4 higher spin algebra contains the $$ \mathcal{N} $$ N = 2 higher spin algebra, as a subalgebra, found by Fradkin and Linetsky some time ago.