  Mirror symmetry relates type IIB string theory on a Calabi-Yau 3-fold to type
IIA on the mirror CY manifold, whose complex structure and Kaehler moduli
spaces are exchanged. We show that the mirror map is a particular case of a
more general quantum equivalence, fractional mirror symmetry, between
Calabi-Yau compactifications and non-CY ones. As was done by Greene and Plesser
for mirror symmetry, we obtain these new dualities by considering orbifolds of
Gepner models, of asymmetric nature, leading to superconformal field theories
isomorphic to the original ones, but with a different target-space
interpretation. The associated Landau-Ginzburg models involve both chiral and
twisted chiral multiplets hence cannot be lifted to ordinary gauged linear
sigma-models.
