Baby Universes, Holography, and the Swampland
Jacob McNamara, Cumrun Vafa
TL;DR
This work addresses how to reconcile Euclidean wormholes with holography in quantum gravity without resorting to ensemble averages in dimensions $d>3$. It proposes the Baby Universe Hypothesis, $\dim \mathcal{H}_{BU}=1$, tying this to swampland constraints that forbid free parameters and global $(-1)$-form symmetries, and interprets the state-operator correspondence to argue against strictly local bulk operators in a UV-complete theory. The authors show that, under these assumptions, factorization and locality in AdS/CFT emerge naturally and that holography can be viewed as Gauss's law for entropy, with the one-dimensional BU Hilbert space enforcing zero entropy for closed universes. They further argue that ensemble holography is a feature of $d=2$ (and perhaps $d=3$) theories, such as JT gravity, which should be realized as brane worldvolume theories in a higher-dimensional quantum-gravity framework without ensembles in $d>3$.
Abstract
On the basis of a number of Swampland conditions, we argue that the Hilbert space of baby universe states must be one-dimensional in a consistent theory of quantum gravity. This scenario may be interpreted as a type of "Gauss's law for entropy" in quantum gravity, and provides a clean synthesis of the tension between Euclidean wormholes and a standard interpretation of the holographic dictionary, with no need for an ensemble. Our perspective relies crucially on the recently-proposed potential for quantum-mechanical gauge redundancies between states of the universe with different topologies. By an application of the state-operator correspondence, this proposal rules out the possibility of nontrivial, strictly well-defined bulk operators supported in a compact region. We further comment on the possible exceptions in $d\leq 3$ for this hypothesis, and the role of an ensemble for holographic theories in low dimensions, such as JT gravity in $d = 2$ and possible cousins in $d=3$. We argue that these examples are incomplete physical theories that should be viewed as branes in a higher dimensional theory of quantum gravity, for which an ensemble plays no role.