The Large N 't Hooft Limit of Kazama-Suzuki Model

TL;DR

This paper explores the structure of N=2 Kazama-Suzuki models on complex projective spaces, constructing higher spin currents, analyzing their algebraic relations, and connecting these to classical W-infinity symmetries in the large N and k limit.

Contribution

It constructs higher spin currents in N=2 W_{N+1} algebra and links their operator product expansions to classical W-infinity algebra in the large N, k limit.

Findings

Construction of higher spin currents with specific spins.

Explicit dependence of self-coupling constants on N and k.

Reproduction of classical W-infinity algebra from quantum operator products.

Abstract

We consider N=2 Kazama-Suzuki model on CP^N=SU(N+1)/SU(N)xU(1). It is known that the N=2 current algebra for the supersymmetric WZW model, at level k, is a nonlinear algebra. The N=2 W_3 algebra corresponding to N=2 was recovered from the generalized GKO coset construction previously. For N=4, we construct one of the higher spin currents, in N=2 W_5 algebra, with spins (2, 5/2, 5/2, 3). The self-coupling constant in the operator product expansion of this current and itself depends on N as well as k explicitly. We also observe a new higher spin primary current of spins (3, 7/2, 7/2, 4). From the behaviors of N=2, 4 cases, we expect the operator product expansion of the lowest higher spin current and itself in N=2 W_{N+1} algebra. By taking the large (N, k) limit on the various operator product expansions in components, we reproduce, at the linear order, the corresponding operator product expansions in N=2 classical W_{\infty}^{cl}[\lambda] algebra which is the asymptotic symmetry of the higher spin AdS_3 supergravity found recently.