Chiral Rings Do Not Suffice: N=(2,2) Theories with Nonzero Fundamental Group

Abstract

The Kahler moduli space of a particular non-simply-connected Calabi-Yau manifold is mapped out using mirror symmetry. It is found that, for the model considered, the chiral ring may be identical for different associated conformal field theories. This ambiguity is explained in terms of both A-model and B-model language. It also provides an apparent counterexample to the global Torelli problem for Calabi-Yau threefolds.

12 pages

References in corpus (10)

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• An N=2 Dual Pair and a Phase Transition
• A Stringy Test of the Fate of the Conifold
• Lectures on D-branes and Sheaves
• Integral Cohomology and Mirror Symmetry for Calabi-Yau 3-folds
• Quantization of Fayet-Iliopoulos Parameters in Supergravity
• Worldsheet Instantons and Torsion Curves, Part B: Mirror Symmetry
• Worldsheet Instantons, Torsion Curves, and Non-Perturbative Superpotentials
• Mirror Symmetry and the Moduli Space for Generic Hypersurfaces in Toric Varieties
• Special Geometry and the Swampland
• Notes on nonabelian (0,2) theories and dualities
• Stable Singularities in String Theory
• Worldsheet Instantons and Torsion Curves, Part A: Direct Computation
• Mirror Symmetry and the Type II String
• Heterotic Instanton Superpotentials from Complete Intersection Calabi-Yau Manifolds
• Non-vanishing Superpotentials in Heterotic String Theory and Discrete Torsion
• A counterexample to the birational Torelli problem for Calabi-Yau threefolds
• Non-vanishing Heterotic Superpotentials on Elliptic Fibrations
• Calabi-Yau threefolds with a curve of singularities and counterexamples to the Torelli problem
• Finding the Mirror of the Beauville Manifold
• Three Generations on the Quintic Quotient
• Notes on a singular Landau-Ginzburg family
• Calabi-Yau threefolds over finite fields and torsion in cohomologies
• Mirror Symmetry of Calabi-Yau Manifolds Fibered by (1,8)-Polarized Abelian Surfaces
• Non-Local Observables in the A-Model