The mathcal{N} = 4 higher spin algebra for generic \u03bc parameter

Abstract

The mathcal{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} = 4 higher spin generators for low spins s1 and s2 (s1 + s2 ≤ 11) explicitly, we determine the complete mathcal{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} = 4 higher spin algebra contains the mathcal{N} = 2 higher spin algebra, as a subalgebra, found by Fradkin and Linetsky some time ago.