MSSM-like models on $ {{\mathbb{Z}}_8} $ toroidal orbifolds

Abstract

We extend the promising heterotic string searches for MSSM-like models to $ {{\mathbb{Z}}_8} $ orbifolds. There exist five inequivalent $ {{\mathbb{Z}}_8} $ toroidal orbifolds distinguished by two types of twists that act on five different torus lattices; one of which cannot be represented as a Lie-algebra root lattice. Contrary to previous investigations, we study the consequences of the different underlying orbifold torus lattices. Therefore, rather than focussing on one particular geometry, we perform systematic model searches on these five $ {{\mathbb{Z}}_8} $ orbifolds simultaneously, taking all possible inequivalent SU(5) and SO(10) gauge shifts as our starting point. We present cumulative tables and figures comparing the chiral SM and vector-like exotic spectra on these geometries.