High-energy scattering in nonconformal gauge theories is investigated using the AdS/conformal field theory (CFT) dual string-gravity theory. It is argued that strong-gravity processes, such as black hole formation, play an important role in the dual dynamics. Further information about this dynamics is found by performing a linearized analysis of gravity for a mass near an infrared brane; this gives the far field approximation to black hole or other strong-gravity effects, and in particular allows us to estimate their shape. From this shape, one can infer a total scattering cross section that grows with center of mass energy as ln(2) E, saturating the Froissart bound.

In gravitational theories with extra dimensions, it is argued that the existence of a positive vacuum energy generically implies catastrophic instability of our four-dimensional world. The most generic instability is a decompactification transition to growth of the extra dimensions, although other equally bad transitions may take place. This follows from simple considerations based on the form of the potential for the size modulus of the extra dimensions, and apparently offers a resolution of the conundrums presented by eternal de Sitter space. This argument is illustrated in the context of string theory with a general discussion of potentials generated by fluxes, wrapped branes, and stringy corrections. Moreover, it is unlikely that the present acceleration of the Universe represents an ongoing transition in a quintessence scenario rolling toward decompactification, unless the higher-dimensional theory has a cosmological constant.

Warped compactifications with branes provide a new approach to the hierarchy problem and generate a diversity of four-dimensional thresholds. We investigate the relationships between these scales, which fall into two classes. Geometrical scales, such as thresholds for Kaluza-Klein, excited string, and black hole production, are generically determined solely by the spacetime geometry. Dynamical scales, notably the scale of supersymmetry breaking and moduli masses, depend on other details of the model. We illustrate these relationships in a class of solutions of type IIB string theory with imaginary self-dual fluxes. After identifying the geometrical scales and the resulting hierarchy, we determine the gravitino and moduli masses through explicit dimensional reduction, and estimate their value to be near the four-dimensional Planck scale. In the process we obtain expressions for the superpotential and Kähler potential, including the effects of warping. We identify matter living on certain branes to be effectively sequestered from the supersymmetry breaking fluxes: specifically, such "visible sector" fields receive no tree-level masses from the supersymmetry breaking. However, loop corrections are expected to generate masses, at the phenomenologically viable TeV scale.