Abelian Landau--Ginzburg Orbifolds and Mirror Symmetry

TL;DR

This paper constructs and analyzes Landau-Ginzburg orbifold models in heterotic string theory, revealing mirror symmetry and new three-generation models through explicit constructions and symmetry analysis.

Contribution

It provides explicit constructions of LG--potentials and orbifolds with abelian symmetries, highlighting mirror symmetry and new phenomenologically interesting models.

Findings

Explicit chiral ring construction for LG vacua

Demonstration of mirror symmetry in the space of theories

Discovery of new three-generation models

Abstract

We construct a class of Heterotic String vacua described by Landau--Ginzburg theories and consider orbifolds of these models with respect to abelian symmetries. For LG--vacua described by potentials in which at most three scaling fields are coupled we explicitly construct the chiral ring and discuss its diagonalization with respect to its most general abelian symmetry. For theories with couplings between at most two fields we present results of an explicit construction of the LG--potentials and their orbifolds. The emerging space of (2,2)--theories shows a remarkable mirror symmetry. It also contains a number of new three--generation models.