Heterotic orbifold models on Lie lattice with discrete torsion

TL;DR

This paper introduces a new class of heterotic orbifold models on non-factorisable Lie lattice tori, classifies their automorphisms and discrete torsion, and finds potential for models with fewer generations of chiral matter.

Contribution

It presents a novel construction of heterotic orbifolds on Lie lattice tori with a comprehensive classification and analysis of their properties, including discrete torsion effects.

Findings

Some models have smaller Euler numbers than factorisable tori models.

Potential for fewer generations of chiral matter fields in these orbifolds.

Classification of abelian orbifolds with and without discrete torsion.

Abstract

We provide a new class of Z_N x Z_M heterotic orbifolds on non-factorisable tori, whose boundary conditions are defined by Lie lattices. Generally, point groups of these orbifolds are generated by Weyl reflections and outer automorphisms of the lattices. We classify abelian orbifolds with and without discrete torsion. Then we find that some of these models have smaller Euler numbers than those of models on factorisable tori T^2 x T^2 x T^2. There is a possibility that these orbifolds provide smaller generation numbers of N=1 chiral matter fields than factorisable models.