UC Santa Barbara

Holography remains one of the most powerful approaches to understanding quantum gravity. The currently best-understood realization of holography is AdS/CFT -- a map between a quantum gravity theory in anti-de Sitter space (AdS) and a conformal field theory (CFT) on its boundary. In this thesis, several aspects of this duality are explored, with a focus on entanglement, chaos and causality. Entanglement plays an especially important role in holography because it is deeply connected to the emergence of spacetime; chaos is another key player in recent developments of holography because it is a characteristic feature of black holes that is expected to persist beyond the classical regime; finally, the idea of causality is a valued concept even in a quantum theory of gravity where the spacetime itself fluctuates, and the boundary CFT which has a well-defined notion of causality is a pragmatic starting point for understanding causality in a bulk theory of quantum gravity. One main theme of the thesis is to explore how these aspects depend on the theory. In particular, conclusions are drawn for whether certain statements that hold in General Relativity hold in general higher-derivative gravity and/or with higher-spin fields. Another theme is the connections between different concepts. In particular, boundary quantities that are apparently very different may be intricately related from the bulk perspective.