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 deter-mined 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.
- Publication:
-
Journal of High Energy Physics
- Pub Date:
- December 2016
- DOI:
- 10.1007/JHEP12(2016)001
- arXiv:
- arXiv:1607.00728
- Bibcode:
- 2016JHEP...12..001A
- Keywords:
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- AdS-CFT Correspondence;
- Conformal and W Symmetry;
- High Energy Physics - Theory
- E-Print:
- 71 pages