Initial Systematic Investigations of the Landscape of Low Layer NAHE Extensions

TL;DR

This paper systematically investigates extensions of the NAHE basis in the WCFFHS formalism, analyzing their gauge groups, matter content, and supersymmetry, revealing correlations and identifying unique three-generation GUT models.

Contribution

It provides the first comprehensive statistical analysis of low-layer NAHE extensions, highlighting their phenomenological features and geometric interpretations.

Findings

More models with enhanced ST SUSY when exceptional groups are present in order-3 extensions.

Identified three-generation GUT models with geometric basis vectors and no rank-cuts.

Statistical correlations between gauge groups and supersymmetry levels.

Abstract

The discovery that the number of physically consistent string vacua is on the order of 10^500 has prompted several statistical studies of string phenomenology. Contained here is one such study that focuses on the Weakly Coupled Free Fermionic Heterotic String (WCFFHS) formalism. Presented are systematic extensions of the well-known NAHE (Nanopoulos, Antoniadis, Hagelin, Ellis) set of basis vectors, which have been shown to produce phenomenologically realistic models. Statistics related to the number of U(1)'s, gauge group factors, non-Abelian singlets, ST SUSYs, as well as the gauge groups themselve are discussed for the full range of models produced as well as models containing GUT groups only. Prior results of other large-scale investigations are compared with these regarding the aforementioned quantities. Statistical coupling between the gauge groups and the number of ST SUSYs is also discussed, and it was found that for order-3 extensions there are more models with enhanced ST SUSY when there is an exceptional group present. Also discussed are some three-generation GUT models found in the data sets. These models are unique because they come from basis vectors which still have a geometric interpretation -- there are no "rank-cuts" in these models.