{"paper":{"title":"Quantum spacetime and quantum fluctuations in the IKKT model at weak coupling","license":"http://creativecommons.org/licenses/by/4.0/","headline":"In the IKKT matrix model, quantum fluctuations of the matrices become negligible compared to the background noncommutativity scale at weak coupling.","cross_cats":[],"primary_cat":"hep-th","authors_text":"Harold C. Steinacker","submitted_at":"2026-05-13T10:07:26Z","abstract_excerpt":"This paper aims to clarify conceptual aspects of emergent structure in IKKT-type matrix models. Even without any adjustable parameters in the action, non-trivial matrix vacua do acquire a meaningful coupling constant, as well as two distinct uncertainty scales: a) the scale of noncommutativity of the matrix background, and b) the scale of quantum fluctuations of the matrices under the path integral. These scales are estimated for two prototypes of matrix backgrounds, known as Moyal-Weyl quantum plane and covariant quantum spacetime. Their relative importance separates two regimes: 1) the semi-"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The quantum fluctuations are shown to be negligible in the weak coupling regime. This justifies previous work on the emergent 3+1-dimensional semi-classical geometry and (quantum) gravity in suitable vacua.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The chosen matrix backgrounds (Moyal-Weyl quantum plane and covariant quantum spacetime) are stable vacua whose scale estimates accurately capture the dominant physics without significant higher-order corrections or instabilities.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"In the IKKT matrix model, quantum fluctuations are negligible compared to noncommutativity scales at weak coupling for Moyal-Weyl and covariant quantum spacetime backgrounds, justifying semi-classical emergent geometry.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"In the IKKT matrix model, quantum fluctuations of the matrices become negligible compared to the background noncommutativity scale at weak coupling.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f1a9bc32ead15cf06a37c359acda991777b92737f70850fed14b2688f4320fe3"},"source":{"id":"2605.13294","kind":"arxiv","version":1},"verdict":{"id":"10be3739-f643-4274-88f8-e7fcd22aa0ff","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:42:18.831928Z","strongest_claim":"The quantum fluctuations are shown to be negligible in the weak coupling regime. This justifies previous work on the emergent 3+1-dimensional semi-classical geometry and (quantum) gravity in suitable vacua.","one_line_summary":"In the IKKT matrix model, quantum fluctuations are negligible compared to noncommutativity scales at weak coupling for Moyal-Weyl and covariant quantum spacetime backgrounds, justifying semi-classical emergent geometry.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The chosen matrix backgrounds (Moyal-Weyl quantum plane and covariant quantum spacetime) are stable vacua whose scale estimates accurately capture the dominant physics without significant higher-order corrections or instabilities.","pith_extraction_headline":"In the IKKT matrix model, quantum fluctuations of the matrices become negligible compared to the background noncommutativity scale at weak coupling."},"references":{"count":52,"sample":[{"doi":"","year":null,"title":"Steinacker,One-loop effective action and emergent gravity on quantum spaces in the IKKT matrix model,JHEP05(2023) 129 [arXiv:2303.08012]","work_id":"9e8844dd-0ed4-4345-943d-20c9d8d22e60","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"Steinacker,Gravity as a quantum effect on quantum space-time,Phys","work_id":"484eed7a-c76c-47fd-afbf-6b13f870606d","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"H. C. Steinacker and T. Tran,Quantumhs-Yang-Mills from the IKKT matrix model, 2405.09804","work_id":"0898b484-9e34-4606-8e9c-9ed23ebc0465","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"A. Manta and H. C. Steinacker,Dynamical Covariant Quantum Spacetime with Fuzzy Extra Dimensions in the IKKT model,2509.24753","work_id":"661cf8f7-1285-4886-9a59-158a1611fd02","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"The emergence of (3+1)-dimensional expanding spacetime from complex Langevin simulations of the Lorentzian type IIB matrix model with deformations","work_id":"f2278b9f-1692-4245-94fb-b8feb5c4a816","ref_index":5,"cited_arxiv_id":"2604.19836","is_internal_anchor":true}],"resolved_work":52,"snapshot_sha256":"4ce28ff79428b42f649e83c778b67bc65151c9c609b5611c4f36bbf6cbd3c26b","internal_anchors":25},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}