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

The large level limit of the $\mathcal{N}=2$ $\mathrm{S}\mathrm{O}(2N)$ Kazama-Suzuki coset models is argued to be equivalent to the orbifold of $4N$ free fermions and bosons by the Lie group $\mathrm{S}\mathrm{O}(2N)\times \mathrm{S}\mathrm{O}(2)$. 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.