The next 16 higher spin currents and three-point functions in the large $$\mathcal{N}=4$$ N = 4 holography

• Main Authors: Changhyun Ahn, Dong-gyu Kim, Man Hea Kim
• Format: Article
• Language: English
• Published: SpringerOpen 2017-08-01
• Series: European Physical Journal C: Particles and Fields
• Online Access: http://link.springer.com/article/10.1140/epjc/s10052-017-5064-6

Abstract By using the known operator product expansions (OPEs) between the lowest 16 higher spin currents of spins $$(1, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, 2,2,2,2,2,2, \frac{5}{2}, \frac{5}{2}, \frac{5}{2}, \frac{5}{2}, 3)$$ ( 1 , 3 2 , 3 2 , 3 2 , 3 2 , 2 , 2 , 2 , 2 , 2 , 2 , 5 2 , 5 2 , 5 2 , 5 2 , 3 ) in an extension of the large $$\mathcal{N}=4$$ N = 4 linear superconformal algebra, one determines the OPEs between the lowest 16 higher spin currents in an extension of the large $$\mathcal{N}=4$$ N = 4 nonlinear superconformal algebra for generic N and k. The Wolf space coset contains the group $$G =\mathrm{SU}(N+2)$$ G = SU ( N + 2 ) and the affine Kac–Moody spin 1 current has the level k. The next 16 higher spin currents of spins $$(2,\frac{5}{2}, \frac{5}{2}, \frac{5}{2}, \frac{5}{2}, 3,3,3,3,3,3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2},4)$$ ( 2 , 5 2 , 5 2 , 5 2 , 5 2 , 3 , 3 , 3 , 3 , 3 , 3 , 7 2 , 7 2 , 7 2 , 7 2 , 4 ) arise in the above OPEs. The most general lowest higher spin 2 current in this multiplet can be determined in terms of affine Kac–Moody spin $$\frac{1}{2}, 1$$ 1 2 , 1 currents. By careful analysis of the zero mode (higher spin) eigenvalue equations, the three-point functions of bosonic higher spin 2, 3, 4 currents with two scalars are obtained for finite N and k. Furthermore, we also analyze the three-point functions of bosonic higher spin 2, 3, 4 currents in the extension of the large $$\mathcal{N}=4$$ N = 4 linear superconformal algebra. It turns out that the three-point functions of higher spin 2, 3 currents in the two cases are equal to each other at finite N and k. Under the large (N, k) ’t Hooft limit, the two descriptions for the three-point functions of higher spin 4 current coincide with each other. The higher spin extension of SO(4) Knizhnik Bershadsky algebra is described.