General Properties of Landscapes: Vacuum Structure, Dynamics and Statistics
Even the simplest extra-dimensional theory, when compactified, can lead to a vast and complex landscape. To make progress, it is useful to focus on generic features of landscapes and compactifications. In this work we will explore universal features and consequences of (i) vacuum structure, (ii) dynamics resulting from symmetry breaking, and (iii) statistical predictions for low-energy parameters and observations. First, we focus on deriving general properties of the vacuum structure of a theory independent of the details of the geometry. We refine the procedure for performing compactifications by proposing a general gauge-invariant method to obtain the full set of Kaluza-Klein towers of fields for any internal geometry. Next, we study dynamics in a toy model for flux compactifications. We show that the model exhibits symmetry-breaking instabilities for the geometry to develop lumps, and suggest that similar dynamical effects may occur generically in other landscapes. The questions of the observed arrow of time as well as the observed value of the neutrino mass lead us to consider statistics within a landscape, and we verify that our observations are in fact typical given the correct vacuum structure and (in the case of the arrow of time) initial conditions. Finally, we address the question of subregion duality in AdS/CFT, arguing for a criterion for a bulk region to be reconstructable from a given boundary subregion by local operators. While of less direct relevance to cosmological space-times, this work provides an improved understanding of the UV/IR correspondence, a principle that underlies the construction of many holographically-inspired measures used to make statistical predictions in landscapes.