All Abelian Symmetries of Landau-Ginzburg Potentials

Details All Abelian Symmetries of Landau-Ginzburg Potentials All Abelian Symmetries of Landau-Ginzburg Potentials

1992-11-11

arxiv.org/abs/hep-th/9211047v2

Nucl.Phys. B405 (1993) 305-325

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1016/0550-3213(93)90549-5

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--H\"ubsch 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.

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