| Ever since Kaluza's remarkable paper in 1921 where he successfully unified Einstein's General Theory of Relativity with Maxwell's Electromagnetism by invoking an extra “fifth” dimension, extra dimensions, i.e. dimensions other than the regularly observed three dimensions of space and one dimension of time, have played an intriguing but often essential role in high energy physics and cosmology. The fundamental reason behind the success of extra dimensions (either mathematical or physical in nature) lies in its ability to “geometrize” symmetries. Symmetries which are algebraically realized in four dimensional theories can be identified with the space-time symmetries or isometries of the extra dimensions and this has several important benefits. For example, one can understand and implement various symmetry breaking mechanisms using the geometric symmetries of the extra dimensions.; In my dissertation, I consider three different problems exploring and utilizing these deep connections between symmetry, symmetry breaking and extra dimensions. In the first problem we show how one can add a “radial coordinate” to deSitter space-times to get a higher dimensional flat space-time. The process can now be inverted to obtain theories on deSitter space-times from known theories on flat space-times. In the second problem, I discuss Kaluza-Klein theories where our universe is considered to be truly higher dimensional in nature. In particular I explore the possibility of explaining symmetry breaking in gauge theories through a transition of the extra dimensional manifold from a more symmetric to a less symmetric metric space. I also consider cosmological implications of such a phase transition. Finally, the last problem concerns harmonic superspace formalism, where one introduces extra fermionic coordinates and “harmonic coordinates” to geometrize supersymmetry and R-symmetry respectively. |
