Landau-Ginzburg orbifolds with discrete torsion

TL;DR

This paper completes the classification of Landau-Ginzburg models with abelian twists and discrete torsion, revealing that discrete torsion introduces few new spectra and does not generally relate to mirror symmetry.

Contribution

It extends the classification of (2,2) vacua from Landau-Ginzburg models to include abelian twists with discrete torsion, showing limited impact on spectra and the non-connection to mirror symmetry.

Findings

Few new spectra arise from discrete torsion.

Mirror symmetry is not generally related to discrete torsion.

The Berglund-Hübsch construction extends naturally to torsion orbifolds.

Abstract

We complete the classification of (2,2) vacua that can be constructed from Landau--Ginzburg models by abelian twists with arbitrary discrete torsions. Compared to the case without torsion the number of new spectra is surprisingly small. In contrast to a popular expectation mirror symmetry does not seem to be related to discrete torsion (at least not in the present compactification framework): The Berglund-H"ubsch construction naturally extends to orbifolds with torsion; for more general potentials, on the other hand, the new spectra neither have nor provide mirror partners in our class of models.