| Symmetry is one of the most important guiding principles in the formulation of modern physical theories and it also plays a major role in determining and constraining the dynamics of such theories. This is particularly true in the context of quantum field theory and string theory. In this thesis, symmetry aspects of two of the most important aspects of these theories are studied, namely black holes and D-branes.;Part II of the thesis focuses on D-branes. In recent years, it has been realized that D-brane dynamics are heavily dominated by their charges. The macroscopic approach to D-brane charges involving K-theory and cohomology only calculates the charge groups, but not the explicit charges of the D-branes. Conformal field theory techniques can be used in a microscopic approach to determine D-brane charges. This calculation is explicitly carried out for a class of Wess-Zumino-Witten models describing string theory on Lie groups. Specifically, the D-brane charges of the group D4 twisted by triality and the group E6 twisted by charge conjugation are calculated explicitly. Along the way a number of non-trivial and surprising Lie theoretic identities are established and proved. The charges are also determined for the D-branes of the non-simply connected group E6/ Z3 twisted by charge conjugation.;Part I of the thesis focuses on several black hole solutions in four and higher dimensions. Specifically, the Kerr-(A)-de Sitter and the Myers-Perry metrics in all dimensions, some charged rotating supergravity black hole solutions in four and five dimensions, and a class of NUT charged black holes in several dimensions are studied. The separability of the Hamilton-Jacobi equation describing the propagation of classical particles and the Klein-Gordon equation describing the propagation of scalar fields in these spacetimes is analyzed. This analysis provides information regarding the spacetime symmetry group, and in many cases, non-trivial Killing tensors are found, whose existence is directly responsible for enhancement of symmetry that permits separation. |
