  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.
