Recent LHC data, together with the electroweak naturalness argument, suggest that the top squarks may be significantly lighter than the other sfermions. We present supersymmetric models in which such a split spectrum is obtained through "geometries": being "close to" electroweak symmetry breaking implies being "away from" supersymmetry breaking, and vice versa. In particular, we present models in 5D warped spacetime, in which supersymmetry breaking and Higgs fields are located on the ultraviolet and infrared branes, respectively, and the top multiplets are localized to the infrared brane. The hierarchy of the Yukawa matrices can be obtained while keeping near flavor degeneracy between the first two generation sfermions, avoiding stringent constraints from flavor and CP violation. Through the AdS/CFT correspondence, the models can be interpreted as purely 4D theories in which the top and Higgs multiplets are composites of some strongly interacting sector exhibiting nontrivial dynamics at a low energy. Because of the compositeness of the Higgs and top multiplets, Landau pole constraints for the Higgs and top couplings apply only up to the dynamical scale, allowing for a relatively heavy Higgs boson, including m h = 125 GeV as suggested by the recent LHC data. We analyze electroweak symmetry breaking for a well-motivated subset of these models, and find that fine-tuning in electroweak symmetry breaking is indeed ameliorated. We also discuss a flat space realization of the scenario in which supersymmetry is broken by boundary conditions, with the top multiplets localized to a brane while other matter multiplets delocalized in the bulk.

Recently, a new framework for describing the multiverse has been proposed which is based on the principles of quantum mechanics. The framework allows for well-defined predictions, both regarding global properties of the universe and outcomes of particular experiments, according to a single probability formula. This provides complete unification of the eternally inflating multiverse and many worlds in quantum mechanics. In this paper we elucidate how cosmological parameters can be calculated in this framework, and study the probability distribution for the value of the cosmological constant. We consider both positive and negative values, and find that the observed value is consistent with the calculated distribution at an order of magnitude level. In particular, in contrast to the case of earlier measure proposals, our framework prefers a positive cosmological constant over a negative one. These results depend only moderately on how we model galaxy formation and life evolution therein.