UC Berkeley

The holographic principle posits that the physics within a region of spacetime can be encoded in degrees of freedom living on its geometric boundary. This principle is most robustly exemplified by the AdS/CFT correspondence, which provides a dictionary between quantum gravitational degrees of freedom in Anti-de Sitter (AdS) spacetime and those of the conformal field theory (CFT) at its asymptotic boundary. Beyond AdS/CFT, the precise structure of holographic encoding is not fully understood. This dissertation, divided into two parts, addresses various aspects of holography beyond AdS/CFT.In Part I, we study how degrees of freedom outside causal horizons holographically encode the spacetime beyond them. We examine the near-horizon mode structure of Schwarzschild and de Sitter horizons and argue that, from the perspective of semiclassical observers whose ability to resolve fine-grained quantum information is inherently limited, the physics beyond the horizon emerges from near-horizon dynamics. We discuss the relationship between this framework and the standard global framework used in AdS/CFT, emphasizing the complementary mechanisms through which they incorporate unitarity and the equivalence principle.In Part II, we investigate the relationship between the geometry of generic spacetime subregions and their quantum information content, as captured by entanglement entropy and computational complexity. We first use the relationship between random tensor networks and fixed-geometry states to motivate a gravitational path integral derivation of the quantum extremal surface prescription for bulk subregions of AdS. In particular, we show that the von Neumann entropy of a bulk subregion is equal to the generalized entropy of the bulk entanglement wedge containing it. We then propose a notion of generalized complexity for bulk subregions as the sum of their volume and the complexity of the semiclassical bulk fields they support. We demonstrate that if the semiclassical complexity is quantified by a codimension-0 measure which satisfies strong subadditivity, then time-like focusing arguments imply a quantum generalization of the strong energy condition, as well an upper bound on the semiclassical complexity of a slice by its volume.