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

TL;DR

This paper derives the operator product expansion of the lowest higher spin current in an N=2 supersymmetric model, revealing its algebraic structure and connection to higher spin AdS_3 supergravity symmetries.

Contribution

It provides the explicit nonlinear operator product expansion of the lowest higher spin current in the N=2 Kazama-Suzuki model on CP^N, including the effects of self-coupling constants.

Findings

Derived the next higher spin current from the lowest one.

Presented the complete nonlinear operator product expansion.

Discussed the large N,k 't Hooft limit and classical algebra.

Abstract

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_{N+1} algebra with N=3 in the supersymmetric WZW model. By incorporating the self-coupling constant of lowest higher spin current 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. 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.