Higher spin currents in the orthogonal coset theory

Abstract

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.