Non-Factorisable Z2 times Z2 Heterotic Orbifold Models and Yukawa Couplings

TL;DR

This paper classifies Z2 x Z2 heterotic orbifold models, analyzing their lattice structures, fixed points, and Yukawa couplings, revealing a range of generation numbers and conditions for model consistency.

Contribution

It provides a comprehensive classification of both factorisable and non-factorisable lattices and derives conditions for Wilson lines and Yukawa couplings in these models.

Findings

Minimum of 6 net generations in standard embedding

Maximum of 48 net generations

Bounds on fixed tori per twisted sector (4 to 16)

Abstract

We classify compactification lattices for supersymmetric Z2 times Z2 orbifolds. These lattices include factorisable as well as non-factorisable six-tori. Different models lead to different numbers of fixed points/tori. A lower bound on the number of fixed tori per twisted sector is given by four, whereas an upper bound consists of 16 fixed tori per twisted sector. Thus, these models have a variety of generation numbers. For example, in the standard embedding, the smallest number of net generations among these classes of models is equal to six, while the largest number is 48. Conditions for allowed Wilson lines and Yukawa couplings are derived.