Explicit construction of fields in orbifolds of products of $\mathcal N=2$ Minimal models of ADE type

We propose the explicit construction of fields in orbifolds of products of $\mathcal N = (2, 2)$ Superconformal minimal models with A-D-E type modular invariants. Such theories have central charge $c=9$ and arise as a compact sector of Superstring compactification. We use spectral flow twisting of fields by the elements of admissible group $G$. We obtain the complete set of fields of the orbifold from the mutual locality and other requirements of the conformal bootstrap. The collection of mutually local primary fields is labelled by the elements of dual group $G$. The permutation of $G$ and $G^*$ is given by the mirror spectral flow construction of the fields and maps the space of states of the original $G$ orbifold onto the space of states of $G$ orbifold. We show that this transformation is by construction a mirror isomorphism of spaces of states.