Higher spin currents in the orthogonal coset theory

In the coset model (DN(1)⊕DN(1),DN(1)) at levels (k₁, k₂) , the higher spin 4 current that contains the quartic WZW currents contracted with a completely symmetric SO(2N) invariant d tensor of rank 4 is obtained. The three-point functions with two scalars are obtained for any finite N and k₂ with k₁= 1. They are determined also in the large N ’t Hooft limit. When one of the levels is the dual Coxeter number of SO(2N), k₁= 2 N- 2 , the higher spin 72 current, which contains the septic adjoint fermions contracted with the above d tensor and the triple product of structure constants, is obtained from the operator product expansion (OPE) between the spin 32 current living in the N= 1 superconformal algebra and the above higher spin 4 current. The OPEs between the higher spin 72,4 currents are described. For k₁= k₂= 2 N- 2 where both levels are equal to the dual Coxeter number of SO(2N), the higher spin 3 current of U(1) charge 43, which contains the six products of spin 12 (two) adjoint fermions contracted with the product of the d tensor and two structure constants, is obtained. The corresponding N= 2 higher spin multiplet is determined by calculating the remaining higher spin 72,72,4 currents with the help of two spin 32 currents in the N= 2 superconformal algebra. The other N= 2 higher spin multiplet, whose U(1) charge is opposite to the one of the above N= 2 higher spin multiplet, is obtained. The OPE between these two N= 2 higher spin multiplets is also discussed.