The N=4 higher spin algebra for generic μ parameter

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 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 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 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 <-> (1 - mu) 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.

Automated summary

In this study, the complete N = 4 higher spin algebra for general mu was determined by explicitly calculating the (anti)commutators between the N = 4 higher spin generators for low spins. It was found that the structure constants involve a linear combination of two different generalized hypergeometric functions, which remain invariant under the transformation mu <-> (1 - mu). Additionally, it was confirmed that the N = 4 higher spin algebra contains the N = 2 higher spin algebra as a subalgebra.