# Higher spin currents in the orthogonal coset theory

The European Physical Journal C, Jun 2017

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.

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Changhyun Ahn. Higher spin currents in the orthogonal coset theory, The European Physical Journal C, 2017, 394, DOI: 10.1140/epjc/s10052-017-4956-9