No Mirror Symmetry in Landau-Ginzburg Spectra!

Abstract

We use a recent classification of non-degenerate quasihomogeneous polynomials to construct all Landau-Ginzburg (LG) potentials for N=2 superconformal field theories with c=9 and calculate the corresponding Hodge numbers. Surprisingly, the resulting spectra are less symmetric than the existing incomplete results. It turns out that models belonging to the large class for which an explicit construction of a mirror model as an orbifold is known show remarkable mirror symmetry. On the other hand, half of the remaining 15\% of all models have no mirror partners. This lack of mirror symmetry may point beyond the class of LG-orbifolds.

17 pages

References in corpus (1)

• Abelian Landau--Ginzburg Orbifolds and Mirror Symmetry

Cited by in corpus (55)

• Exact Results for N=2 Compactifications of Heterotic Strings
• Calabi-Yau fourfolds for M- and F-Theory compactifications
• Mirror Symmetry, Mirror Map and Applications to Complete Intersection Calabi-Yau Spaces
• PALP: A Package for Analyzing Lattice Polytopes with Applications to Toric Geometry
• Anomaly Cancellation in Six Dimensions
• GKZ-Generalized Hypergeometric Systems in Mirror Symmetry of Calabi-Yau Hypersurfaces
• Duality Between the Webs of Heterotic and Type II Vacua
• 5d and 4d SCFTs: Canonical Singularities, Trinions and S-Dualities
• Toric Geometry and Enhanced Gauge Symmetry of F-Theory/Heterotic Vacua
• Mirror Symmetry for Calabi-Yau Hypersurfaces in Weighted P_4 and Extensions of Landau Ginzburg Theory
• (0,2) Mirror Symmetry
• Periods for Calabi--Yau and Landau--Ginzburg Vacua
• Comment on the Generation Number in Orbifold Compactifications
• Calabi-Yau 4-folds and toric fibrations
• Landau-Ginzburg Orbifolds, Mirror Symmetry and the Elliptic Genus
• The Mirror Map for Invertible LG Models
• Searching for K3 Fibrations
• The (0,2) Exactly Solvable Structure of Chiral Rings, Landau-Ginzburg Theories and Calabi-Yau Manifolds
• The web of Calabi-Yau hypersurfaces in toric varieties
• Landau-Ginzburg Vacua of String, M- and F-Theory at c=12
• 1-Form Symmetry, Isolated N=2 SCFTs, and Calabi-Yau Threefolds
• Mirror Symmetry and the Moduli Space for Generic Hypersurfaces in Toric Varieties
• Toric complete intersections and weighted projective space
• Machine Learning Calabi-Yau Hypersurfaces
• The RR charges of A-type Gepner models
• On the Connectedness of the Moduli Space of Calabi--Yau Manifolds
• PALP - a User Manual
• Conifold Transitions and Mirror Symmetries
• Unification of M- and F- Theory Calabi-Yau Fourfold Vacua
• Mirror Symmetry for Hypersurfaces in Weighted Projective Space and Topological Couplings
• Accidents in (0,2) Landau-Ginzburg theories
• Heterotic Gauge Structure of Type II K3 Fibrations
• All Weight Systems for Calabi-Yau Fourfolds from Reflexive Polyhedra
• Persistent Homology and String Vacua
• Low energy supersymmetry from R-symmetries
• On Periods for String Compactifications
• ADE string vacua with discrete torsion
• ORBIFOLDS WITH DISCRETE TORSION AND MIRROR SYMMETRY
• Geometric Kac-Moody Modularity
• Landau-Ginzburg skeletons
• Dualities and phase transitions for Calabi-Yau 3folds and 4folds
• A modularity test for elliptic mirror symmetry
• The making of Calabi-Yau spaces: Beyond toric hypersurfaces
• Mirror symmetry for quasi-smooth Calabi-Yau hypersurfaces in weighted projective spaces
• Strings on Calabi--Yau spaces and Toric Geometry
• Fano hypersurfaces and Calabi-Yau supermanifolds
• Calabi-Yau Four/Five/Six-folds as ${\mathbb{P}}_{\text{w}}^n$ Hypersurfaces: Machine Learning, Approximation, and Generation
• On Semi-Periods
• Calabi-Yau manifolds and sporadic groups
• Small Landau-Ginzburg theories
• Max Kreuzer's Contributions to the Study of Calabi-Yau Manifolds
• (0,2) string compactifications
• Scaling Behavior in String Theory
• Where are the Mirror Manifolds?
• A Note On ADE String Compactifications