Where are the Mirror Manifolds?
arXiv:hep-th/9303015 · doi:10.1016/0370-2693(93)91318-H
Abstract
The recent classification of Landau--Ginzburg potentials and their abelian symmetries focuses attention on a number of models with large positive Euler number for which no mirror partner is known. All of these models are related to Calabi--Yau manifolds in weighted $\IP_4$, with a characteristic structure of the defining polynomials. A closer look at these potentials suggests a series of non-linear transformations, which relate the models to configurations for which a construction of the mirror is known, though only at certain points in moduli space. A special case of these transformations generalizes the $\ZZ_2$ orbifold representation of the invariant, implying a hidden symmetry in tensor products of minimal models.
(Note and reference added, eqs.15/16 corrected) 12 pages, LaTeX, CERN-TH.6802/93