The Holographic Principle and the Emergence of Spacetime
Results within string theory and quantum gravity suggest that spacetime is not fundamental but rather emergent, with the fundamental degrees of freedom living on a boundary surface of one lower dimension than the bulk. This thesis is devoted to studying the holographic principle and its realization for spacetimes with both negative and positive cosmological constant.
The holographic principle is most explicitly realized in the context of the AdS/CFT correspondence. We examine the extent to which AdS/CFT realizes the holographic principle and study the UV/IR relation. We study aspects of how bulk locality emerges within AdS/CFT. To this effect, we study how to reconstruct the bulk from boundary data. We study how such a reconstruction procedure is sensitive to large changes in the bulk geometry. We study if it is possible to reconstruct a subset of the bulk from a subset of the boundary data. We explore both local and nonlocal CFT quantities as probes of the bulk. One nonlocal quantity is entanglement entropy, and to this effect we construct a framework for computing entanglement entropy within the field theory.
The most ambitious application of the holographic principle would be finding the holographic dual to the multiverse. We investigate properties of this putative duality. We extend the UV/IR relation of AdS/CFT to the multiverse, with the UV cutoff of the theory on future infinity being dual to a late time cutoff (measure) in the bulk. We compare various measure proposals and examine their predictions.