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This thesis reports on aspects of semiclassical gravity with an eye towards holography.Chapter 2 introduces a perturbatively traversable wormhole in a particular four-dimensional quotient spacetime, where traversability is ensured by the Casimir energy of bulk fermions. We compute the fermionic contribution to the integrated null stress-energy tensor and find hints that traversability holds at all times.Chapters 3 and 4 report on computations of entanglement negativity, a multipartite entanglement measure which distinguishes between classical and quantum correlations. We compute holographic entanglement negativity in a toy model of Jackiw-Teitelboim gravity with end-of-the-world branes, finding a rich phase structure which includes replica symmetry breaking in a large region of phase space. We also compute entanglement negativity in a toy model of chaotic eigenstates, finding some qualitative agreement with phase transitions in the holographic model.Chapter 5 describes a modification to random tensor networks to incorporate bulk gauge symmetries which we term the "gauged random tensor network." We find an area operator valued in the center of the gauged random tensor network bulk algebra which more closely resembles the area operator provided by the quantum-corrected Ryu-Takayanagi formula.

Holographic dualities like AdS/CFT provide a non-perturbative definition of a bulk theory of quantum gravity in terms of a lower-dimensional boundary quantum field theory. Elucidating quantum gravity thus becomes the challenge of deciphering the dictionary between bulk and boundary physics, and using it to translate basic properties of the latter into lessons about the former. A crucial intermediary between these two realms is the gravitational path integral, which defines the bulk theory in terms of an integral over spacetimes subject to conditions from the boundary theory. Though shallowly understood and rather formal, this piece of technology has thus far been able to provide deep insights into quantum gravity. This thesis is organized in three parts, each focusing on a different basic property in quantum theory and its consequences for quantum gravity through the gravitational path integral: entanglement, causality, and factorization. Part I addresses the emergence of spacetime from entanglement, with a focus on understanding constraints on the entanglement structure of quantum states to posses classical geometries as holographic bulk duals. These constraints can be expressed as linear inequalities and used to define the holographic entropy cone (HEC). A systematic study of the HEC is accomplished by reformulating the holographic computation of von Neumann entropies as a graph-theoretic one, thereby recasting a complicated problem in differential geometry as a purely combinatorial one. This allows to prove important properties of the HEC, devise proof methods and algorithms for constructing it, derive precise relations to other polytope structures, and ultimately pursue a top-down understanding of the HEC from the universal quantum inequality of subadditivity. This part concludes with an exploration of how the machinery involved in the study of the HEC may also be generalized to settings where the von Neumann entropy receives contributions from bulk quantum fields, a regime where the graph-theoretic apparatus has to be upgraded.Part II presents an alternative perspective on spacetime emergence, both in classical and quantum regimes, based on causality. Starting at a classical level, we explain how the conformal bulk geometry can be reconstructed by encoding its causal structure in data accessible from the boundary field theory. Through the use of field theory correlators, we propose a method for obtaining the full-dimensional bulk geometry up to a conformal factor. This generalizes the approach to bulk metric reconstruction based on light-cone cuts to a prescription which allows for recovering even those dimensions which become compact asymptotically. Moving away from the classical limit, we then resolve a known puzzle that arises from a tension between the bulk and boundary causal structures when the bulk theory is understood as a genuine gravitational path integral over spacetimes.Finally, part III delves into the consequences of the lack of factorization that occurs in holography when wormholes are included in the gravitational path integral. In particular, we study generating functionals in quantum gravity and propose a recipe for their computation which accounts for the contribution of such connected topologies. This allows to differentiate between quenched and annealed quantities in quantum gravity, a distinction which may be used as a consistency test-ground for foundational aspects of the gravitational path integral regarding summing over topologies.

There has been a resurgence of interest in wormholes, and continued growth in the study of primordial black holes, opening up new questions about these objects and their possible existence in our universe. Recent papers demonstrate a new way of forming wormholes in the early universe, via collapsing inflationary bubbles. On our end, these wormholes would take the form of primordial black holes. This lends new interest to an intriguing and largely unaddressed question of what happens to a wormhole as the black hole on each end of it Hawking evaporates. Primordial wormholes would have an early period of traversability and we find, using calculations based on a semi-classical model of Hawking radiation, that as they evaporate they become traversable again to some degree. They then could evaporate to leave a Planck-size wormhole that may or may not persist. We also explore the implications of traversable wormholes and the questions that arise from their existence.

We argue that one can nucleate a traversable wormhole via a nonperturbative process in quantum gravity. To support this, we construct spacetimes in which there are instantons giving a finite probability for a test cosmic string to break and produce two particles on its ends. One should be able to replace the particles with small black holes with only small changes to the spacetime away from the horizons. The black holes are then created with their horizons identified, so this is an example of nucleating a wormhole. Unlike previous examples where the created black holes accelerate apart, in our case they remain essentially at rest. This is important since wormholes become harder and harder to make traversable as their mouths become widely separated, and since traversability can be destroyed by Unruh radiation. In our case, back-reaction from quantum fields can make the wormhole traversable., Comment: 24 pages, 6 Figs, v2: comment added and a few typos corrected

Maldacena and Susskind have proposed a correspondence between wormholes and entanglement, dubbed ER=EPR. We study this in the context of 3d topological quantum field theory, where we show that the formation of a wormhole is the same process as creating a particle-antiparticle pair. A key feature of the ER=EPR proposal is that certain apparently entangled degrees of freedom turn out to be the same. We name this phenomenon "fake entanglement", and show how it arises in our topological quantum field theory model., Comment: 12 pages