The operator product expansions in the N= 4 orthogonal Wolf space coset model

Some of the operator product expansions (OPEs) between the lowest SO(4) singlet higher spin-2 multiplet of spins (2,52,52,52,52,3,3,3,3,3,3,72,72,72,72,4) in an extension of the large N= 4 (non)linear superconformal algebra were constructed in the N= 4 superconformal coset SO(N+4)SO(N)×SO(4) theory with N= 4 previously. In this paper, by rewriting the above OPEs with N= 5 , the remaining undetermined OPEs are completely determined. There exist additional SO(4) singlet higher spin-2 multiplet, six SO(4) adjoint higher spin-3 multiplets, four SO(4) vector higher spin-72 multiplets, SO(4) singlet higher spin-4 multiplet and four SO(4) vector higher spin-92 multiplets in the right hand side of these OPEs. Furthermore, by introducing the arbitrary coefficients in front of the composite fields in the right hand sides of the above complete 136 OPEs, the complete structures of the above OPEs are obtained by using various Jacobi identities for generic N. Finally, we describe them as one single N= 4 super OPE between the above lowest SO(4) singlet higher spin-2 multiplet in the N= 4 superspace.