Investigation of the String Landscape in the Free Fermionic Heterotic String formalism via an Extended Gauge Framework

Finding at least one String model, out of the extremely large landscape of vacua, that uniquely resembles our observable universe is a central problem in String phenomenology and is critical to making progress in String theory. An effort to explore this landscape of String vacua via systematic construction of all consistent 4d String theories using free world-sheet fermions has been made in [1], [2], [3] and [4]. This model building process has been made more efficient in [5] via the use of high-performance computing (HPC). Here, we will focus on the Weakly Coupled Free Fermionic Heterotic String (WCFFHS) construction formalism in [1-4] with emphasis on the gauge framework presented in [5]. We extend the framework in [5], making the model building approach more robust and encompassing. We explicitly construct all layer 1 extended gauge models up to order 28 in four large spacetime dimensions and present an overview of this model building process. Statistics for both 4d N=4 and N=0 SUSY models, with particular emphasis on the gauge groups' ranks and combinations, are presented.