ORBIFOLDS WITH DISCRETE TORSION AND MIRROR SYMMETRY

For a large class of N = 2 SCFTs, which includes minimal models and ma ny sigma models on Calabi-Yau manifolds, the mirror theory can be obta ined as an orbifold. We show that in such a situation the construction of the minor can be extended to the presence of discrete torsions. In the case of the Z(2) x Z(2) torus orbifold, discrete torsion between the two generators directly provides the mirror model. Working at the Gepner point it is, however, possible to understand this mirror pair a s a special case of the Berglund-Hubsch construction. This seems to in dicate that the Z(2) x Z(2) example is a mere coincidence, due to spec ial properties of Z(2) twists, rather than a hint at a new mechanism f or mirror symmetry.