Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Baby Universes and Worldline Field Theories

Eduardo Casali, Donald Marolf, Henry Maxfield, Mukund Rangamani

TL;DR

The work analyzes how to build quantum-gravity Hilbert spaces from path integrals over topologies, focusing on discrete choices that yield abelian baby-universe algebras versus non-abelian QFT-like algebras. By explicitly constructing one-dimensional (worldline) gravity models in Euclidean and Lorentzian flavors, it identifies where QFT-like boundary operator algebras arise as deviations from the Marolf 2020 BU framework. The paper highlights how the inner product, adjoint structure, and boundary-condition prescriptions shape the resulting algebraic structure, showing that ESTs and GATs fit a common abelian BU picture, while naive QFT-like constructions generally fail positivity unless additional ordering or restrictions are imposed. It further discusses generalizations to graphs, higher dimensions, and dynamical boundaries (spacetime D-branes), and frames these discrete choices as guiding principles for connecting wormhole physics with familiar QFT and gravitational intuitions. Overall, the results clarify when wormhole-induced boundary data lead to commuting BU observables and when they can produce richer, non-abelian operator algebras, with implications for interpreting low-dimensional topological models and the role of topology change in quantum gravity.

Abstract

The quantum gravity path integral involves a sum over topologies that invites comparisons to worldsheet string theory and to Feynman diagrams of quantum field theory. However, the latter are naturally associated with the non-abelian algebra of quantum fields, while the former has been argued to define an abelian algebra of superselected observables associated with partition-function-like quantities at an asymptotic boundary. We resolve this apparent tension by pointing out a variety of discrete choices that must be made in constructing a Hilbert space from such path integrals, and arguing that the natural choices for quantum gravity differ from those used to construct QFTs. We focus on one-dimensional models of quantum gravity in order to make direct comparisons with worldline QFT.

Baby Universes and Worldline Field Theories

TL;DR

The work analyzes how to build quantum-gravity Hilbert spaces from path integrals over topologies, focusing on discrete choices that yield abelian baby-universe algebras versus non-abelian QFT-like algebras. By explicitly constructing one-dimensional (worldline) gravity models in Euclidean and Lorentzian flavors, it identifies where QFT-like boundary operator algebras arise as deviations from the Marolf 2020 BU framework. The paper highlights how the inner product, adjoint structure, and boundary-condition prescriptions shape the resulting algebraic structure, showing that ESTs and GATs fit a common abelian BU picture, while naive QFT-like constructions generally fail positivity unless additional ordering or restrictions are imposed. It further discusses generalizations to graphs, higher dimensions, and dynamical boundaries (spacetime D-branes), and frames these discrete choices as guiding principles for connecting wormhole physics with familiar QFT and gravitational intuitions. Overall, the results clarify when wormhole-induced boundary data lead to commuting BU observables and when they can produce richer, non-abelian operator algebras, with implications for interpreting low-dimensional topological models and the role of topology change in quantum gravity.

Abstract

The quantum gravity path integral involves a sum over topologies that invites comparisons to worldsheet string theory and to Feynman diagrams of quantum field theory. However, the latter are naturally associated with the non-abelian algebra of quantum fields, while the former has been argued to define an abelian algebra of superselected observables associated with partition-function-like quantities at an asymptotic boundary. We resolve this apparent tension by pointing out a variety of discrete choices that must be made in constructing a Hilbert space from such path integrals, and arguing that the natural choices for quantum gravity differ from those used to construct QFTs. We focus on one-dimensional models of quantum gravity in order to make direct comparisons with worldline QFT.

Paper Structure

This paper contains 27 sections, 49 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Boundary observables and Baby Universes
  3. One-dimensional Theories of Gravity
  4. Amplitudes from the sum over one-dimensional spacetimes
  5. The matter theory
  6. Mini-superspace models
  7. Euclidean Statistical Theories
  8. The amplitudes
  9. The baby universe Hilbert space
  10. Generalizations
  11. Euclidean approach to QFT-like theories
  12. Hilbert space construction
  13. Null states
  14. Operator algebra
  15. Generalizations
  16. ...and 12 more sections

Figures (3)

  • Figure 1: Schematic illustration of a spacetime wormhole connecting three boundaries.
  • Figure 2: Slicing open a quantum amplitude to reveal the bra and ket components.
  • Figure 3: