This work is concerned with the study of several ten-dimensional field theories intimately associated with superstring theories, and possibilities for obtaining realistic four-dimensional theories from them.
Three chapters follow the N = 2b supergravity from ten to five, then to four dimensions . First of all, compactifications to five dimensions on various manifolds are studied. Then the entire mass spectrum for the compactification on S5 is derived using techniques of harmonic analysis on spheres. A particular set of modes corresponds to a gauged maximal super gravity theory in five dimensions; this theory, with Yang-Mills group SO(6), is constructed in detail. By a process similar to analytic continuation, noncompact versions of this theory are also obtained, gauging all the semisimple real forms of SO(6). One particular form, with gauge group SO*(6) ≈ SU(3,1), compactifies to fiat four-dimensional spacetime and offers attractive phenomenological possibilities.
The final chapter is concerned with candidates for effective low-energy theories for N = 1 superstrings with gauge group SO(32) or E8 x E8. These effective theories contain curvature squared terms, and require unusual gravitational interactions to cancel anomalies. The field equations are derived and found to admit compactifications to fiat four dimensional spacetime, with the possibility of accommodating many phenomenological considerations.
