This paper proposes a new, non-perturbative way to think about quantum gravity. The authors argue that a simple topological theory called BF theory, with gauge group SO(d+1,1), can act as a universal "skeleton" or sewing kit. By insisting that physical amplitudes do not depend on how one cuts and glues spacetime — a gluing or sewing consistency condition — one can in principle bootstrap bulk quantum gravity theories, including the familiar AdS/CFT examples and ideas that appear in spin-foam models.

At a conceptual level, the bootstrap principle here is presentation independence: if you cut a spacetime in different ways and recombine the pieces, the resulting physical answers must agree. The authors formulate this within a defect-closed BF sewing calculus. That calculus includes Wilson lines (objects that carry charge along curves), codimension-two monodromy defects (places where fields pick up a twist when you go around them), and junctions where these ingredients meet. The paper treats BF theory as a universal toolkit that supplies the possible ways to change how amplitudes are presented; the actual choice of which pieces are combined is fixed by the physical data one is trying to bootstrap.

The proposal also gives a concrete picture for how boundary geometry and candidate quantum microstates appear. On one branch of the BF theory, a flat BF connection (a field configuration with zero curvature) encodes the conformal geometry of a boundary. Wilson-line path integrals then serve to build candidate bulk microstates and charge sectors. Remarkably, the authors argue that ordinary perturbative bulk fields can still show up even though the BF skeleton is topological: towers of Wilson lines labeled by multi-trace operators reproduce known one-loop determinants in thermal AdS. They also point out that the BF Fourier kernel plays a role similar to the modular S-matrix familiar from two-dimensional conformal field theory.