Baby Universes, Holography, and the Swampland

TL;DR

This paper argues that in consistent quantum gravity theories, the Hilbert space of baby universe states is one-dimensional, implying a 'Gauss's law for entropy' and challenging the need for an ensemble in holography.

Contribution

It introduces a new perspective based on Swampland conditions and gauge redundancies that constrains the structure of baby universe states and bulk operators in quantum gravity.

Findings

Hilbert space of baby universes must be one-dimensional in consistent theories

No nontrivial, well-defined bulk operators supported in compact regions

Ensembles in low-dimensional holography are incomplete theories viewed as branes

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.