The large level limit of Kazama-Suzuki models

TL;DR

This paper investigates the large level limit of N=(2,2) superconformal Kazama-Suzuki models, revealing their connection to continuous orbifolds and providing a detailed spectrum analysis relevant for AdS3/CFT2 dualities.

Contribution

It determines the boundary conditions and bulk spectrum of the limit theories, confirming their identification as the orbifold C^n/U(n) in the context of higher-spin AdS3/CFT2 duality.

Findings

Full bulk spectrum of N=2 super-W_{n+1} primaries obtained

Boundary conditions in the limit theories characterized

Identification of the limit theory as C^n/U(n) orbifold confirmed

Abstract

Limits of families of conformal field theories are of interest in the context of AdS/CFT dualities. We explore here the large level limit of the two-dimensional N=(2,2) superconformal W_{n+1} minimal models that appear in the context of the supersymmetric higher-spin AdS3/CFT2 duality. These models are constructed as Kazama-Suzuki coset models of the form SU(n+1)/U(n). We determine a family of boundary conditions in the limit theories, and use the modular bootstrap to obtain the full bulk spectrum of N=2 super-W_{n+1} primaries in the theory. We also confirm the identification of this limit theory as the continuous orbifold C^n/U(n) that was discussed recently.