Some Comments on Wormholes and Factorization

  Spacetime wormholes have played an important role in recent progress in black hole physics. However, in the context of AdS/CFT, these wormholes lead to a basic puzzle: the "factorization problem", introduced by Maldacena and Maoz. In this talk we will explore this issue in some simple models, including Marolf and Maxfield's topological model, JT gravity, and the SYK model. These models are described by ensemble averages of quantum systems; the factorization problem is solved by focusing on single members of the ensemble. In gravitational theories like JT gravity and the topological model, this involves introducing many additional spacetime boundaries in path integral computations. We find that there is a simple effective description common to these models, where the many additional boundaries are replaced by a single "dynamical" boundary. A variant of this effective description also applies to the SYK model. This effective description involves a peculiar modification to the sum over geometries; it requires us to identify a ``diagonal'' subset of the contributions of the dynamical boundaries with the wormhole. This rule has somewhat different origins in the full description of the gravitational theories and the SYK model. We briefly comment on how this might be relevant to conventional, non-averaged AdS/CFT.