The Mirror Map for Invertible LG Models

Abstract

Calculating the (a,c) ring of the maximal phase orbifold for `invertible' Landau--Ginzburg models, we show that the Berglund--H"ubsch construction works for all potentials of the relevant type. The map that sends a monomial in the original model to a twisted state in the orbifold representation of the mirror is constructed explicitly. Via this map, the OP selection rules of the chiral ring exactly correspond to the twist selection rules for the orbifold. This shows that we indeed arrive at the correct point in moduli space, and that the mirror map can be extended to arbitrary orbifolds, including non-abelian twists and discrete torsion, by modding out the appropriate quantum symmetries.

10 pages, latex, CERN-TH.7165/94 and TUW-94/01

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• Mirror Symmetry and the Moduli Space for Generic Hypersurfaces in Toric Varieties
• Toric complete intersections and weighted projective space
• A Landau--Ginzburg mirror theorem without concavity
• Orbifold E-functions of dual invertible polynomials
• D-brane central charge and Landau-Ginzburg orbifolds
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• ORBIFOLDS WITH DISCRETE TORSION AND MIRROR SYMMETRY
• FJRW-Rings and Landau-Ginzburg Mirror Symmetry in Two Dimensions
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• Strings on Calabi--Yau spaces and Toric Geometry
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• Heterotic (0,2) Gepner Models and Related Geometries
• Counting charged massless states in the (0,2) heterotic CFT/geometry connection
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• A Landau-Ginzburg mirror theorem via matrix factorizations
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• Hodge diamonds of the Landau--Ginzburg orbifolds
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• Gamma integral structure for an invertible polynomial of chain type
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• Mirror Symmetry and the Web of Landau-Ginzburg String Vacua