Mirror symmetry and the moduli space for generic hypersurfaces in toric varieties

Per Berglund, Sheldon Katz, Albrecht Klemm

Research output: Contribution to journalArticlepeer-review


The moduli dependence of (2,2) superstring compactifications based on Calabi-Yau hypersurfaces in weighted projective space has so far only been investigated for Fermat-type polynomial constraints. These correspond to Landau-Ginzburg orbifolds with c = 9 whose potential is a sum of A-type singularities. Here we consider the generalization to arbitrary quasi-homogeneous singularities at c = 9. We use minor symmetry to derive the dependence of the models on the complexified Kähler moduli and check the expansions of some topological correlation functions against explicit genus zero and genus one instanton calculations. As an important application we give examples of how non-algebraic ("twisted") deformations can be mapped to algebraic ones, hence allowing us to study the full moduli space. We also study how moduli spaces can be nested in each other, thus enabling a (singular) transition from one theory to another. Following the recent work of Greene, Morrison and Strominger we show that this corresponds to black hole condensation in type II string theories compactified on Calabi-Yau manifolds.

Original languageEnglish (US)
Pages (from-to)153-204
Number of pages52
JournalNuclear Physics, Section B
Issue number1-2
StatePublished - Dec 4 1995
Externally publishedYes

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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