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We explore the construction and stability of asymptotically anti-de Sitter Euclidean wormholes in a variety of models. In simple ad hoc low-energy models, it is not hard to construct two-boundary Euclidean wormholes that dominate over disconnected solutions and which are stable (lacking negative modes) in the usual sense of Euclidean quantum gravity. Indeed, the structure of such solutions turns out to strongly resemble that of the Hawking-Page phase transition for AdS-Schwarzschild black holes, in that for boundary sources above some threshold we find both a `large' and a `small' branch of wormhole solutions with the latter being stable and dominating over the disconnected solution for large enough sources. We are also able to construct two-boundary Euclidean wormholes in a variety of string compactifications that dominate over the disconnected solutions we find and that are stable with respect to field-theoretic perturbations. However, as in classic examples investigated by Maldacena and Maoz, the wormholes in these UV-complete settings always suffer from brane-nucleation instabilities (even when sources that one might hope would stabilize such instabilities are tuned to large values). This indicates the existence of additional disconnected solutions with lower action. We discuss the significance of such results for the factorization problem of AdS/CFT., Comment: 88 pages, 16 figures and 1 table

We study phases of equilibrium Hawking radiation in d-dimensional holo- graphic CFTs on spatially compact spacetimes with two black holes. In the particular phases chosen the dual (d + 1)-dimensional bulk solutions describe a variety of black fun- nels and droplets. In the former the CFT readily conducts heat between the two black holes, but it in the latter such conduction is highly suppressed. While the generic case can be understood in certain extreme limits of parameters on general grounds, we focus on CFTs on specific geometries conformally equivalent to a pair of d ≥ 4 AdS d -Schwarzschild black holes of radius R. Such cases allow perturbative analyses of non-uniform funnels associated with Gregory-Laflamme zero-modes. For d = 4 we construct a phase diagram for pure funnels and droplets by constructing the desired bulk solutions numerically. The fat non-uniform funnel is a particular interesting phase that dominates at small R (due to having lowest free energy) despite being sub-dominant in the perturbative regime. The uniform funnel dominates at large R, and droplets and thin funnels dominate at certain intermediate values. The thin funnel phase provides a mystery as it dominates over our other phases all that way to a critical Rturn beyond which it fails to exist. The free energy of the system thus appears to be discontinuous at Rturn, but such discontinuities are for- bidden by the 2nd law. A new more-dominant phase is thus required near Rturn but the nature of this phase remains unclear.