Undecidability in spacetime geometry via the AdS/CFT correspondence
Abstract
Undecidability, a hallmark of Gödel incompleteness theorems, has recently emerged in quantum many-body physics through the spectral gap problem. We demonstrate how this logical limitation can be holographically transmitted to a class of gravitational theories via the AdS/CFT correspondence. By embedding a translationally invariant spin Hamiltonian with undecidable gap status into a large-N gauge theory, we generate an anti–de Sitter (AdS) dual in which the selection of dominant bulk saddle (Poincaré AdS or AdS soliton) is itself undecidable. Consequently, under standard semiclassical holographic assumptions, even determining which smooth spacetime geometry emerges from quantum gravity can be beyond the limits of computability.
Fields of Study & Subjects
Black Holes and Theoretical Physics
Noncommutative and Quantum Gravity Theories
Advanced Operator Algebra Research
Publication details
- Journal / source
- Physical review. D/Physical review. D.
- Publisher
- American Physical Society (APS)
- Volume
- 113
- Issue
- 2
- Publication date
- 9 January 2026
- Language
- EN