Where are the Mirror Manifolds?

Details Where are the Mirror Manifolds? Where are the Mirror Manifolds?

1993-03-03

arxiv.org/abs/hep-th/9303015v2

Phys.Lett. B314 (1993) 31-40

Physics

High Energy Physics

High Energy Physics - Theory

(Note and reference added, eqs.15/16 corrected) 12 pages, LaTeX, CERN-TH.6802/93

Scientific paper

10.1016/0370-2693(93)91318-H

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 $D$ invariant, implying a hidden symmetry in tensor products of minimal models.

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