Conformal bootstrap and Mirror symmetry of states in Gepner models

We consider two explicit constructions of states in the orbifolds of a product of Minimal $N=(2,2)$ models which are based on twisting by spectral flow, mutual locality and operator algebra requirement. It is shown that these two constructions lead to the Berglund-Hubsh-Krawitz dual orbifold groups which define mirror pairs of isomorphic models. Then we generalize our construction for the orbifolds of Gepner models of superstring compactification and explicitly build IIA/IIB mirror map of the space of states of the superstrings using light-cone gauge.