Branes, strings and black holes

In this dissertation we study various non perturbative gauge theories in two spatial dimensions. We also explore problems of gravitational collapse in AdS/CFT and high energy scattering in M-theory. We begin by studying scattering of D0 branes in eleven dimensional supergravity (SUGRA) using the tree level four point amplitude. We compare the rate of annihilation of D0 − D¯0 branes to the rate of elastic D0 − D¯0 scattering and find that the former is always smaller than the latter.; Next, we use dielectric branes to find non singular string theory duals of a perturbed 2+1 dimensional gauge theory living on D2 branes.; Then, we investigate the oblique vacua in the perturbed 2+1 dimensional gauge theory living on D2 branes. We show that D4 charge is an essential ingredient in understanding D2 → NS5 polarizations. We find that some of the polarization states, which appear as metastable vacua, when D4 charge is not considered, are in fact unstable. They decay by acquiring D4 charge, tilting and shrinking to zero size.; Turning to the Condensed Matter Physics, we investigate the stability of the classical ground state of the Quantum Hall Soliton recently proposed in hepth/0010105. We explore two possible perturbations, which are not spherically symmetric, and we find that the potential energy decreases in both case.; Finally, we provide examples of gravitational collapse and black hole formation in AdS, either from collapsing matter shells or in analogy to the Oppenheimer-Sneider solution. We then investigate boundary properties of the corresponding states. In particular, we describe the boundary two point function corresponding to a shell outside its horizon; if the shell is quasistatically lowered into the horizon, the resulting state is the Boulware state. (Abstract shortened by UMI.)...