[Paper Review] Baby Universes, Holography, and the Swampland

Jacob McNamara, Cumrun Vafa|arXiv (Cornell University)|Apr 14, 2020

Black Holes and Theoretical Physics38 references59 citations

TL;DR

The paper argues that in spacetime dimensions greater than three, the baby universe Hilbert space is one-dimensional, ruling out alpha-parameters and bulk operators, and explaining holography without ensembles except in low dimensions where such ensembles are viewed as/branes in higher-dimensional theories.

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.

Motivation & Objective

• Motivate swampland constraints on quantum gravity by analyzing baby universes and alpha-parameters.
• Propose the Baby Universe Hypothesis (dim H_BU = 1) as a resolution to unitarity and factorization issues from Euclidean wormholes.
• Show that alpha-parameters correspond to a global (-1-form) symmetry, conflicting with no-global-symmetries in quantum gravity.
• Demonstrate how the Baby Universe Hypothesis implies absence of strictly local bulk operators.
• Discuss implications for holography, including AdS/CFT locality, ensemble interpretations in low dimensions, and a Gauss’s law for entropy perspective.

Proposed method

• Review Coleman’s alpha-parameters and their relation to coupling constants in the Euclidean path integral.
• Describe the proposed gauge redundancies between baby universe states and the construction of the alpha-eigenstate Hilbert space.
• Argue from swampland principles that no free parameters and no global (-1)-form symmetries imply a one-dimensional H_BU.
• Apply state-operator correspondence to argue absence of strictly well-defined bulk operators in a complete quantum gravity.
• Map implications onto holography: standard AdS/CFT dictionary, boundary locality, and factorization in the presence/absence of ensembles.

Experimental results

Research questions

• RQ1 Do alpha-parameters lead to a genuine ensemble of theories in quantum gravity in d>3?
• RQ2 Can gauge redundancies collapse the baby universe Hilbert space to a single state in d>3?
• RQ3 What are the consequences of a one-dimensional H_BU for unitarity and information?
• RQ4 Are there strictly well-defined bulk operators in a complete quantum gravity theory?
• RQ5 How does the Baby Universe Hypothesis reshape holography and the role of ensembles across dimensions?

Key findings

• The authors argue that in d>3 quantum gravity, H_BU should be one-dimensional, leaving only the Hartle-Hawking state.
• Alpha-parameters behave as global (-1)-form symmetries and would imply free parameters, which is incompatible with no-free-parameters swampland constraints.
• Global (-1)-form symmetries cannot exist in quantum gravity for d>3, which supports the Baby Universe Hypothesis.
• A bulk operator strictly localized in a compact region cannot be well-defined under the Baby Universe Hypothesis; only boundary observables remain strictly well-defined.
• Ensembles in holography are natural only in d=2 or possibly d=3 theories (e.g., JT gravity), but not expected for d>3, where such ensembles are interpreted as brane-worldvolume effects in a higher-dimensional theory.
• Holography can be viewed as Gauss’s law for entropy, with factorization explained by gauge redundancies rather than ensembles.