Phenomenological Study of a Class of Heterotic String Compactifications

String theory has the potential of unifying the strong, weak, electromagnetic, and gravitational interactions. The classical solutions of string theory correspond to two dimensional conformal field theories. Without a nonperturbative formulation to dynamically determine which classical solution corresponds to the ground state, one is left to study all of them. The hope is that realistic low energy phenomenology will result from one model and it will be the chosen one in a more fundamental formulation. In this thesis we study a class of phenomenologically promising heterotic string models, due to Gepner, that are based on the minimal N = 2 superconformal field theories. The effective four dimensional theory is N = 1 supergravity coupled to Yang -Mills with a visible sector gauge group including E _6 with massless chiral fermions in the 27 dimensional representation of E_6. The generation number in these models is too large to be realistic but can be reduced, along with the gauge group, in orbifold models. We perform a systematic analysis of the class of orbifold models based on the diagonal modular invariant in the minimal model sector. We find among this class one four generation model and begin a phenomenological analysis by constructing the superpotential in the specific case where there is an rm SU_{C }(3)otimes SU_{L}(2)otimes SU_{R}(2)otimes U^{ '}(1)otimes U^{' '}(1) visible sector gauge group. Assuming that supersymmetry is broken via soft supersymmetry breaking terms we minimize the effective potential and find that gauge symmetry breaking first occurs at a scale of approximately 10^{15} Gev where the U(1)^{''} part of the gauge group is broken.