Phenomenological Analysis of Heterotic Strings: Non-abelian Constructions and Landscape Studies

String theory offers the unique promise of unifying all the known forces in nature. However, the internal consistency of the theory requires that spacetime have more than four dimensions. As a result, the extra dimensions must be compactified in some manner and how this compactification takes place is critical for determining the low-energy physical predictions of the theory. In this thesis we examine two distinct consequences of this fact.First, almost all of the prior research in string model-building has examined the consequences of compactifying on so-called ``abelian'' orbifolds.However, the most general class of compactifications, namely those onnon-abelian orbifolds, remains almost completely unexplored. This thesis focuses on the low-energy phenomenological consequences of compactifying strings on non-abelian orbifolds. One of the main interests in pursuing these theories is that they can, in principle, naturally give rise tolow-energy models which simultaneously have N=1 super symmetry along with scalar particles transforming in the adjoint of the gauge group. These features,which are exceedingly difficult to achieve through abelian orbifolds,are exciting because they are the key ingredients in understanding how grand unification can emerge from string theory.Second, the need to compactify gives rise to a huge ``landscape'' of possible resulting low-energy phenomenologies. One of the goals of the landscape program in string theory is then to extract information about the space of string vacua in the form of statistical correlations between phenomenological features that are otherwise uncorrelated in field theory. Such correlations would thus represent features of string theory that hold independently of a vacuum-selection principle. In this thesis, we study statistical correlations between two features which are likely to be central to any potential description of nature at high-energy scales: gauge symmetries and spacetime supersymmetry. We analyze correlations between these two kinds of symmetry within the context of perturbative heterotic string vacua, and find a number of striking features. We find, for example, that the degree of spacetime supersymmetry is strongly correlated with the probabilities of realizing certain gauge groups, with unbroken supersymmetry at the string scale tending to favor gauge-group factors with larger rank. We also find that nearly half of the heterotic landscape is nonsupersymmetric and yet tachyon-free at tree level; indeed, less than a quarter of the tree-level heterotic landscape exhibits any supersymmetry at all at the string scale