Universality of completeness in quantum gravity

Establish whether the completeness hypothesis—that every charge allowed by Dirac quantization is realized by physical states—is indeed a universal feature of all consistent theories of quantum gravity across the entire landscape, thereby determining if spectral completeness holds generically in any weakly coupled ultraviolet completion of gravity.

Background

Completeness posits that all allowed charges are realized by states in a theory, and is closely tied to expectations about the absence of exact global symmetries in quantum gravity. The paper develops a bottom-up, scattering-based methodology that proves charge completeness in broad classes of theories under specific assumptions. This open conjecture concerns the generality of completeness across all consistent quantum-gravitational theories, beyond the specific cases addressed.

Clarifying the universality of completeness would connect the authors’ constructive scattering approach to broader swampland considerations and foundational principles in quantum gravity. A definitive resolution would determine whether completeness is an intrinsic property of the quantum-gravity landscape rather than a model-dependent feature.