The $\mathfrak{so}$-Kazama-Suzuki Models at Large Level

TL;DR

This paper investigates the large level limit of $ ext{SO}(2N)$ Kazama-Suzuki models, demonstrating their equivalence to an orbifold of free fermions and bosons, and clarifying the structure of twisted sectors and their correspondence to coset representations.

Contribution

It establishes the equivalence between large level Kazama-Suzuki models and a specific orbifold of free fields, including detailed analysis of twisted sectors and their coset representation correspondence.

Findings

Large level limit corresponds to an orbifold of free fields.

Untwisted sector matches a closed subsector of the coset theory.

Twisted sector ground states are identified with coset representations.

Abstract

The large level limit of the $\mathcal{N}=2$ ${\rm SO}(2N)$ Kazama-Suzuki coset models is argued to be equivalent to the orbifold of $4N$ free fermions and bosons by the Lie group ${\rm SO}(2N) \times {\rm SO}(2)$. In particular, it is shown that the untwisted sector of the continuous orbifold accounts for a certain closed subsector of the coset theory. Furthermore, the ground states of the twisted sectors are identified with specific coset representations, and this identification is checked by various independent arguments.