Higher Spin Currents in the Enhanced N=3 Kazama-Suzuki Model

Abstract

The N=3 Kazama-Suzuki model at the `critical' level has been found by Creutzig, Hikida and Ronne. We construct the lowest higher spin currents of spins (3/2, 2,2,2,5/2, 5/2, 5/2, 3) in terms of various fermions. In order to obtain the operator product expansions (OPEs) between these higher spin currents, we describe three N=2 OPEs between the two N=2 higher spin currents denoted by (3/2, 2, 2, 5/2) and (2, 5/2, 5/2, 3) (corresponding 36 OPEs in the component approach). Using the various Jacobi identities, the coefficient functions appearing on the right hand side of these N=2 OPEs are determined in terms of central charge completely. Then we describe them as one single N=3 OPE in the N=3 superspace. The right hand side of this N=3 OPE contains the SO(3)-singlet N=3 higher spin multiplet of spins (2, 5/2, 5/2, 5/2, 3,3,3, 7/2), the SO(3)-singlet N=3 higher spin multiplet of spins (5/2, 3,3,3, 7/2, 7/2, 7/2, 4), and the SO(3)-triplet N=3 higher spin multiplets where each multiplet has the spins (3, 7/2, 7/2, 7/2, 4,4,4, 9/2), in addition to N=3 superconformal family of the identity operator. Finally, by factoring out the spin-1/2 current of N=3 linear superconformal algebra generated by eight currents of spins (1/2, 1,1,1, 3/2, 3/2, 3/2, 2), we obtain the extension of so-called SO(3) nonlinear Knizhnik Bershadsky algebra.

arXiv comment71 pages; The second-fourth paragraphs in page 31 and Appendix H added and to appear in JHEP

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Cited by in corpus (10)

• 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
• The $\mathcal{N}=4$ Coset Model and the Higher Spin Algebra
• Higher Spin Currents in the Orthogonal Coset Theory
• A Supersymmetric Enhancement of $\mathcal{N}=1$ Holographic Minimal Model
• Adding Complex Fermions to the Grassmannian-like Coset Model
• The Operator Product Expansions in the $\mathcal{N}=4$ Orthogonal Wolf Space Coset Model
• The Grassmannian-like Coset Model and the Higher Spin Currents
• Higher Spin Currents with Manifest $SO(4)$ Symmetry in the Large $\mathcal{N}=4$ Holography
• Fermionic Construction in the Supersymmetric Coset Model