Towards a systematic investigation of weakly coupled free fermionic heterotic string gauge group statistics

We investigate several issues regarding weakly coupled free fermionic heterotic string model building. After reviewing the necessary background, we first address an alternative interpretation of the GSO projection in terms of the Weyl conditions on the root space of the gauge group of a given model. We develop an algorithm to systematically generate and analyze string models very efficiently by linearizing the constraints. Next we investigate free fermionic model building from the approach of quantum computing algorithms. We also consider a few unique and interesting gauge groups which can arise in non-standard ways using this method. Then we develop a variation of the well known "NAHE" basis of (quasi)-realistic models with initial observable sector gauge group SO(10) that offers the possibility of a new class of models with an initial observable sector gauge group of E6. Finally we consider several topics regarding the applications of Optical Unification in string models.