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Fractional Mirror Symmetry

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.