Mirror Symmetry and the Moduli Space for Generic Hypersurfaces in Toric Varieties

Abstract

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 mirror 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.

54 pages, use harvmac and epsf, one uuencoded figure

References in corpus (19)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Phases of $N=2$ Theories In Two Dimensions
• Simple Singularities and N=2 Supersymmetric Yang-Mills Theory
• Holomorphic Anomalies in Topological Field Theories
• Mirror Symmetry for Two Parameter Models -- II
• Mirror Symmetry for Two Parameter Models -- I
• Calabi-Yau Moduli Space, Mirror Manifolds and Spacetime Topology Change in String Theory
• A Generalized Construction of Mirror Manifolds
• Mirror Symmetry, Mirror Map and Applications to Complete Intersection Calabi-Yau Spaces
• Considerations of One-Modulus Calabi-Yau Compactifications: Picard-Fuchs Equations, Kähler Potentials and Mirror Maps
• Periods and Duality Symmetries in Calabi-Yau Compactifications
• Landau-Ginzburg String Vacua
• No Mirror Symmetry in Landau-Ginzburg Spectra!
• Landau-Ginzburg Orbifolds, Mirror Symmetry and the Elliptic Genus
• The Mirror Map for Invertible LG Models
• Chiral Rings Do Not Suffice: N=(2,2) Theories with Nonzero Fundamental Group
• All Abelian Symmetries of Landau-Ginzburg Potentials
• Mirror Symmetry for Hypersurfaces in Weighted Projective Space and Topological Couplings
• Recent Efforts in the Computation of String Couplings:

Cited by in corpus (31)

• Calabi-Yau fourfolds for M- and F-Theory compactifications
• Black Holes and Solitons in String Theory
• Enhanced Gauge Symmetry in Type II String Theory
• Explicit de Sitter Flux Vacua for Global String Models with Chiral Matter
• F-theory fluxes, Chirality and Chern-Simons theories
• Mirror Symmetry, N=1 Superpotentials and Tensionless Strings on Calabi-Yau Four-Folds
• Duality Between the Webs of Heterotic and Type II Vacua
• Topological String Amplitudes, Complete Intersection Calabi-Yau Spaces and Threshold Corrections
• A Calabi-Yau Database: Threefolds Constructed from the Kreuzer-Skarke List
• Strong Coupling Singularities and Non-abelian Gauge Symmetries in $N=2$ String Theory
• Non-Perturbative Properties of Heterotic String Vacua Compactified on $K3\times T^2$
• New Higgs Transitions between Dual N=2 String Models
• Geometric Transitions
• Holomorphic Couplings in String Theory
• Five-Brane Superpotentials and Heterotic/F-theory Duality
• The web of Calabi-Yau hypersurfaces in toric varieties
• Worldsheet Instantons and Torsion Curves, Part B: Mirror Symmetry
• Small Flux Superpotentials for Type IIB Flux Vacua Close to a Conifold
• Type II/F-theory Superpotentials with Several Deformations and N=1 Mirror Symmetry
• Toric Methods in F-theory Model Building
• Enhanced Symmetries in Multiparameter Flux Vacua
• Geometric transitions between Calabi-Yau threefolds related to Kustin-Miller unprojections
• Elliptic Blowup Equations for 6d SCFTs. IV: Matters
• A Note on Computations of D-brane Superpotential
• Dualities and phase transitions for Calabi-Yau 3folds and 4folds
• Exact Solutions of Exceptional Gauge Theories from Toric Geometry
• On D0-branes in Gepner models
• On Semi-Periods
• Mirror Symmetry, D-brane Superpotential and Ooguri-Vafa Invariants of Compact Calabi-Yau Manifolds
• Mirror Symmetry and the Web of Landau-Ginzburg String Vacua
• Catalysis of proton decay in superstring theory