Dimensionally Reduced Landau-Ginzburg Orbifolds with Discrete Torsion

TL;DR

This paper shows that many higher-dimensional $(2,2)$ string vacua can be reformulated as Landau-Ginzburg orbifolds with discrete torsion, simplifying their geometric interpretation to complex 3-folds with specific properties.

Contribution

It demonstrates a unifying reformulation of a broad class of string vacua as Landau-Ginzburg orbifolds with discrete torsion, reducing the number of superfields to five.

Findings

Reformulation of $(2,2)$ vacua as Landau-Ginzburg orbifolds with discrete torsion

Reduction of superfields from n>5 to n=5 in the orbifold description

Geometric interpretation as complex 3-folds with vanishing first Chern class

Abstract

It is observed that a large class of $(2,2)$ string vacua with $n>5$ superfields can be rewritten as Landau_Ginzburg orbifolds with discrete torsion and $n=5$. The naive geometric interpretation (if one exists) would be that of a complex 3-fold, not necessarily K\"ahler but still with vanishing first Chern class.