String effective actions, dualities, and generating solutions

This thesis covers in general two separate topics: the string e®ective actions and the geodesic motion of brane solutions. The main theme of the ¯rst topic, i.e., the string e®ective actions, is the construction of the abelian D-brane e®ective action. In the limit of constant ¯eld strengths this action is known as the Born-Infeld action. In this thesis we propose a new method for constraining the four dimensional D-brane e®ective action and applied to the abelian case with derivative corrections. The method is based on the electromagnetic duality invariance. We show that selfduality requirement only constrains the derivative corrections terms to the Born-Infeld theory but not determines them. In the second topic of this thesis we consider the geodesic motion on the symmetric moduli spaces that arise after timelike and spacelike reductions of (super)gravity theories. The geodesics correspond to timelike respectively spacelike p-brane solutions when they are lifted over a p-dimensional °at space. In particular, we consider the problem of constructing the minimal generating solution : a geodesic with the minimal number of free parameters such that all other geodesics are generated through isometries G: This way we ¯nd the most general °uxless Sp-brane solution of Einstein gravity with (deformed) worldvolume via the reduction over an Euclidean torus. In case we reduce over a Lorentzian torus, the target space becomes a pseudo-Riemannian G=H¤ with H¤ is a non-compact real form. Correspondingly, the geodesic solutions on G=H¤ are labeled by the sign of the a±ne velocity jjvjj2: We derive the generating solution for cosets GL(r + s)=SO(r; s); and give the Einstein vacuum solutions that can be obtained from uplifting a SL(n;R)=SO(n¡1; 1) stationary (¡1)-brane solution.