Quantum Gravity from Gluing Consistency: AdS/CFT to Spin-Foams

Abstract

We argue that BF theory with $SO(d+1,1)$ gauge group provides a SymTFT ''skeleton'' for building AdS$_{d+1}$/CFT$_d$ pairs via gluing consistency as the bootstrap principle, loosely analogous to how compact Chern-Simons theory is a TQFT skeleton for rational CFTs. This is a non-perturbative $bulk$ framework for quantum gravity. The bootstrap is formulated as presentation independence of physical amplitudes within a universal, defect-closed BF sewing calculus, which includes Wilson lines, codimension-two monodromy defects, and their junctions. The flat BF connection encodes the conformal geometry of the boundary, while Wilson-line path integrals construct candidate quantum-gravity microstates and charge sectors. When the bootstrapped spectrum has a stress tensor, Ward identities naturally connect it to the $B$-field, a relation we call generalized simplicity. In large-$N$, large-gap regimes admitting a gravitational EFT, this motivates the introduction of an effective notion of the $B$-field. In the Einstein limit, this becomes the ''simplicity'' relation used in spin-foam models. Conventional spin-foam models reach gravity by constraining BF theory. We suggest instead that BF theory is the Platonic sewing skeleton, from which theories are to be bootstrapped. Despite the topological nature of the skeleton, perturbative local bulk fields can emerge via Wilson-towers of multi-trace primaries, reproducing their one-loop determinants. We note that the BF Fourier kernel is a suggestive higher-dimensional analogue of the modular-$S$ structure. Because the bulk gluing principle in itself does not require a boundary description, the framework is conceptually broader than AdS/CFT. We sketch how de Sitter space may fit into this picture, with a natural role for observers. Our approach elevates gluing consistency to a universal bulk principle underlying theories of quantum gravity.