All Abelian Symmetries of Landau-Ginzburg Potentials

Abstract

We present an algorithm for determining all inequivalent abelian symmetries of non-degenerate quasi-homogeneous polynomials and apply it to the recently constructed complete set of Landau--Ginzburg potentials for $N=2$ superconformal field theories with $c=9$. A complete calculation of the resulting orbifolds without torsion increases the number of known spectra by about one third. The mirror symmetry of these spectra, however, remains at the same low level as for untwisted Landau--Ginzburg models. This happens in spite of the fact that the subclass of potentials for which the Berglund--Hübsch construction works features perfect mirror symmetry. We also make first steps into the space of orbifolds with $\ZZ_2$ torsions by including extra trivial fields.

21 pages, LaTeX, CERN-TH.6705/92

References in corpus (3)

• A Generalized Construction of Mirror Manifolds
• On the Classification of Quasihomogeneous Functions
• Abelian Landau--Ginzburg Orbifolds and Mirror Symmetry

Cited by in corpus (27)

• Mirror Symmetry, Mirror Map and Applications to Calabi-Yau Hypersurfaces
• PALP: A Package for Analyzing Lattice Polytopes with Applications to Toric Geometry
• Topological String Amplitudes, Complete Intersection Calabi-Yau Spaces and Threshold Corrections
• On the Classification of Reflexive Polyhedra
• Calabi-Yau 4-folds and toric fibrations
• The Mirror Map for Invertible LG Models
• Searching for K3 Fibrations
• Lectures on Mirror Symmetry
• Complete classification of reflexive polyhedra in four dimensions
• The web of Calabi-Yau hypersurfaces in toric varieties
• Mirror Symmetry and the Moduli Space for Generic Hypersurfaces in Toric Varieties
• Toward the M(F)--Theory Embedding of Realistic Free-Fermion Models
• Toric complete intersections and weighted projective space
• Mirror Symmetry for Hypersurfaces in Weighted Projective Space and Topological Couplings
• Heterotic Gauge Structure of Type II K3 Fibrations
• All Weight Systems for Calabi-Yau Fourfolds from Reflexive Polyhedra
• Persistent Homology and String Vacua
• ADE string vacua with discrete torsion
• ORBIFOLDS WITH DISCRETE TORSION AND MIRROR SYMMETRY
• LG/CY correspondence: the state space isomorphism
• On genus-0 invariants of Calabi-Yau hybrid models
• The making of Calabi-Yau spaces: Beyond toric hypersurfaces
• Reflexive polyhedra, weights and toric Calabi-Yau fibrations
• Heterotic (0,2) Gepner Models and Related Geometries
• Strings on Calabi--Yau spaces and Toric Geometry
• On the Elliptic Genus and Mirror Symmetry
• A global mirror symmetry framework for the Landau-Ginzburg/Calabi-Yau correspondence