1208.0058 (Changhyun Ahn)

The Operator Product Expansion of the Lowest Higher Spin Current at
Finite N    [PDF]

Changhyun Ahn

For the N=2 Kazama-Suzuki(KS) model on CP^3, the lowest higher spin current with spins (2, 5/2, 5/2, 3) is obtained from the generalized GKO coset construction. By computing the operator product expansion of this current and itself, the next higher spin current with spins (3, 7/2, 7/2, 4) is also derived. This is a realization of the N=2 W_4 algebra with N=3 in the supersymmetric WZW model. By incorporating the self-coupling constant which is known for the general (N,k), we present the complete nonlinear operator product expansion of the lowest higher spin current with spins (2, 5/2, 5/2, 3) in the N=2 KS model on CP^N space. Definitely, this should coincide with the asymptotic symmetry of the higher spin AdS_3 supergravity at the quantum level. The large (N,k) 't Hooft limit and the corresponding classical nonlinear algebra are also discussed.

View original: http://arxiv.org/abs/1208.0058