Higher Spin Currents in Wolf Space for Generic N

Abstract

We obtain the 16 higher spin currents with spins (1,3/2,3/2,2),(3/2, 2,2, 5/2), (3/2,2,2, 5/2) and (2,5/2,5/2,3) in the N=4 superconformal Wolf space coset SU(N+2)/[SU(N) x SU(2) x U(1)]. The antisymmetric second rank tensor occurs in the quadratic spin-1/2 Kac-Moody currents of the higher spin-1 current. Each higher spin-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-1/2 and spin-1 Kac-Moody currents respectively. Moreover, the remaining higher spin currents of spins 2, 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 N=4 nonlinear superconformal algebra.

49 pages, The V^e in the last equation of page 10 corrected and the epsilon^{ijk} inserted at the second equation of page 34 and to appear in JHEP

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Cited by in corpus (12)

• Higher Spin Currents in the N=2 Stringy Coset Minimal Model
• Higher Spin Currents in Wolf Space: Part III
• The $\mathcal{N}=4$ Coset Model and the Higher Spin Algebra
• Higher Spin Currents in the Enhanced N=3 Kazama-Suzuki Model
• The $\mathcal{N}=4$ Higher Spin Algebra for Generic $\mu$ Parameter
• The Next $16$ Higher Spin Currents and Three-Point Functions in the Large $\mathcal{N}=4$ Holography
• Three Point Functions in the N=4 Orthogonal Coset Theory
• Higher Spin Currents in the Orthogonal Coset Theory
• The Operator Product Expansions in the $\mathcal{N}=4$ Orthogonal Wolf Space Coset Model
• Adding Complex Fermions to the Grassmannian-like Coset Model
• Wolf Space Coset Spectrum in the Large $\mathcal{N}=4$ Holography
• Higher Spin Currents with Manifest $SO(4)$ Symmetry in the Large $\mathcal{N}=4$ Holography