Classical Vacua of String Theory: Chiral Bosonic Representations.

The equations of constraint that arise from requiring a consistent first quantization of string theory (bosonic, supersymmetric, or heterotic) have an enormous number of solutions. Each solution may be interpreted as a classical vacuum of the second-quantized string field theory. This thesis will focus on the family of string vacua that have a representation as the superconformal field theory of chiral bosons. To motivate the discussion, we use the path integral formulation to explain the connection between first-quantized strings and two-dimensional conformal field theories. We present a superspace quantization for the superstring, and explain the special role of the one-loop string amplitude. This amplitude may be recast as the partition function for the superconformal field theory of chiral bosons on a cylinder. Solutions to first-quantized string theory can now be constructed within the operator formulation of two-dimensional conformal field theory. The starting point of this construction is the two-dimensional super-Virasoro algebra of chiral bosons. We present a series of bosonized supercurrents that are consistent solutions to this algebra. The use, and importance, of the cocycles involved in the definition of such supercurrents is clarified. The supercurrent, which is the generator of two-dimensional supersymmetry, also determines a large part of the spacetime physics of the string vacua, or string models, thereby created. Examples of this construction are given. We explain the role played by the supercurrent in introducing simply-laced symmetry in string models. The choice of the supercurrent can ensure, or prevent, the appearance of spacetime supersymmetry in a string model besides influencing the interaction couplings of the string model. Finally, we demonstrate the utility of the chiral bosonic representation in linking various schemes proposed for the construction of consistent string models. This family of vacua is shown to include toroidal compactifications of ten-dimensional strings, asymmetric orbifolds, the spin structure construction of string models, and even certain N = (2,2) compactifications on group manifolds. Considering that this class includes several examples with semi-realistic phenomenology, the possibility that the preferred vacuum lies within it is not entirely improbable. Nevertheless, we feel that the significance of our work lies in the conclusions we draw from this study about the structure of the space of solutions to first-quantized string theory, of which the chiral bosonic representations are only a subset.