Dualities in Supergravity and Solvable Lie Algebras

The purpose of the present thesis is to give a self-contained review of the solvable Lie algebra approach to supergravity problems related with S, T and U dualities. After recalling the general features of dualities in both Superstring theory and Supergravity, we introduce the solvable Lie algebra formalism as an alternative description of the scalar manifold in a broad class of supergravity theories. It is emphasized how this mathematical technique on one hand allows to achieve a geometrical intrinsic characterization of Ramond-Ramond, Neveu-Schwarz and Peccei-Quinn scalars, once the supergravity theory is interpreted as the low energy limit of a suitably compactified superstring theory, on the other hand provides a convenient framework in which to deal with several non-perturbative problems. Using solvable Lie algebras for instance we find a general mechanism for spontaneous N=2 to N=1 local supersymmetry breaking. Moreover solvable Lie algebras are used to define a general method for studying systematically BPS saturated Black Hole solutions in supergravity.