For this JC, I will review the recently much debated puzzles that arise in holographic systems with baby universes. After describing the original set-up of Antonini-Sasieta-Swingle, I will explain the paradox raised by Antonini-Rath, which suggests the existence of a single CFT state that can have two distinct holographic descriptions in the bulk: one with a closed baby universe and one without. I will discuss various proposed resolutions of this puzzle, which may (or may not) require us to rethink the holographic dictionary in AdS/CFT.

I will review an elegant, theory-independent argument that proves the existence of exactly marginal operators in the presence of a conformal manifold. The proof relies on a few technical assumptions, which I will discuss in detail. The rest of the discussion will be phrased in terms of conformal interfaces separating two CFTs on the conformal manifold, which we take as an opportunity to discuss the fundamentals of defect CFTs. The overarching topic into which this result fits is that of proving certain (AdS) swampland conjectures from CFT principles.