Undecidability in spacetime geometry via the AdS/CFT correspondence
Year: 2026
Authors: Mir S.A., Marino F., Shabir A., Krauss L.M., Faizal M.
Autors Affiliation: Jamia Millia Islamia, Dept Phys, New Delhi 110025, India; Asian Sch Business, Dept Comp Sci, Noida 201303, Uttar Pradesh, India; CNR, Ist Nazl Ott, Via Sansone 1, I-50019 Sesto Fiorentino, FI, Italy; INFN, Sez Firenze, Via Sansone 1, I-50019 Sesto Fiorentino, FI, Italy; Canadian Quantum Res Ctr, 204-3002 32 Ave, Vernon, BC V1T 2L7, Canada; Origins Project Fdn, Phoenix, AZ 85028 USA; Univ British Columbia Okanagan, Irving K Barber Sch Arts & Sci, Kelowna, BC V1V 1V7, Canada; Univ Durham, Dept Math Sci, Stockton Rd, Durham DH1 3LE, England; Hasselt Univ, Fac Sci, Agoralaan Gebouw D, B-3590 Diepenbeek, Belgium.
Abstract: Undecidability, a hallmark of G & ouml;del incompleteness theorems, has recently emerged in quantum manybody 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 (Poincare 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.
Journal/Review: PHYSICAL REVIEW D
Volume: 113 (2) Pages from: L021904-1 to: L021904-7
KeyWords: Field-theories; Quantum; StabilityDOI: 10.1103/zqgf-6qp7
