Baby universes and worldline field theories

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