# Higher spin currents in Wolf space for generic N

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Journal of High Energy Physics

, 2014:109

First Online: 16 December 2014Received: 04 November 2014Accepted: 04 December 2014 Abstract

We obtain the 16 higher spin currents with spins \ \left1,\frac{3}{2},\frac{3}{2},2 ight \, \ \left\frac{3}{2},2,2,\frac{5}{2} ight \, \ \left\frac{3}{2},2,2,\frac{5}{2} ight \ and \ \left2,\frac{5}{2},\frac{5}{2},3 ight \ in the \ \mathcal{N}=4 \ superconformal Wolf space coset \ \frac{\mathrm{SU}\leftN+2 ight}{\mathrm{SU}N\times \mathrm{S}\mathrm{U}2\times \mathrm{U}1} \. The antisymmetric second rank tensor occurs in the quadratic spin- \ \frac{1}{2} \ Kac-Moody currents of the higher spin-1 current. Each higher spin- \ \frac{3}{2} \ current contains the above antisymmetric second rank tensor and three symmetric and traceless second rank tensors i.e. three antisymmetric almost complex structures contracted by the above antisymmetric tensor in the product of spin- \ \frac{1}{2} \ and spin-1 Kac-Moody currents respectively. Moreover, the remaining higher spin currents of spins \ 2,\frac{5}{2},3 \ contain the combinations of the symmetric metric, the three almost complex structures, the antisymmetric tensor or the three symmetric tensors in the multiple product of the above Kac-Moody currents as well as the composite currents from the large \ \mathcal{N}=4 \ nonlinear superconformal algebra.

KeywordsAdS-CFT Correspondence Conformal and W Symmetry ArXiv ePrint: 1411.0356

Autor: Changhyun Ahn - Hyunsu Kim