Higher spin currents in the orthogonal coset theory

In the coset model $$(D_N^{(1)} \oplus D_N^{(1)},D_N^{(1)})$$ at levels $$(k_1,k_2)$$, 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 $$k_2$$ with $$k_1=1$$. They are determined also in the large N ’t Hooft limit. When one of the levels is the dual Coxeter number of SO(2N), $$k_1=2N-2$$, the higher spin $$\frac{7}{2}$$ 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 $$\frac{3}{2}$$ current living in the $$\mathcal{N}=1$$ superconformal algebra and the above higher spin 4 current. The OPEs between the higher spin $$\frac{7}{2}, 4$$ currents are described. For $$k_1=k_2=2N-2$$ where both levels are equal to the dual Coxeter number of SO(2N), the higher spin 3 current of U(1) charge $$\frac{4}{3}$$, which contains the six products of spin $$\frac{1}{2}$$ (two) adjoint fermions contracted with the product of the d tensor and two structure constants, is obtained. The corresponding $$\mathcal{N}=2$$ higher spin multiplet is determined by calculating the remaining higher spin $$\frac{7}{2}, \frac{7}{2}, 4$$ currents with the help of two spin $$\frac{3}{2}$$ currents in the $$\mathcal{N}=2$$ superconformal algebra. The other $$\mathcal{N}=2$$ higher spin multiplet, whose U(1) charge is opposite to the one of the above $$\mathcal{N}=2$$ higher spin multiplet, is obtained. The OPE between these two $$\mathcal{N}=2$$ higher spin multiplets is also discussed