Undecidability in Spacetime Geometry via the AdS/CFT Correspondence
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911410867404800 |
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| author | Mir, Sameer Ahmad Marino, Francesco Shabir, Arshid Krauss, Lawrence M. Faizal, Mir |
| author_facet | Mir, Sameer Ahmad Marino, Francesco Shabir, Arshid Krauss, Lawrence M. Faizal, Mir |
| contents | 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 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_22761 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Undecidability in Spacetime Geometry via the AdS/CFT Correspondence Mir, Sameer Ahmad Marino, Francesco Shabir, Arshid Krauss, Lawrence M. Faizal, Mir High Energy Physics - Theory General Relativity and Quantum Cosmology 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 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. |
| title | Undecidability in Spacetime Geometry via the AdS/CFT Correspondence |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2601.22761 |