Non Abelian orbifold compactifications of the heterotic string

I consider the construction of heterotic orbifold models based on a toroidal orbifold with non Abelian point group. I construct an explicit model based on the point group $S_3$ and calculate the spectrum and remnant symmetries. This model provides a simple example of rank reduction of the Yang–Mills gauge group directly in the string theory rather than in the effective field theory.