{"paper":{"title":"All $2D$ generalised dilaton theories from $d\\geq 4$ gravities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Reductions of pure gravities in d ≥ 4 dimensions yield all generic two-dimensional Horndeski theories.","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Johanna Borissova","submitted_at":"2026-03-06T19:00:00Z","abstract_excerpt":"We demonstrate that generic two-dimensional Horndeski theories can arise from the reduction of pure gravities in $d \\geq 4$ dimensions, and therefore generic onshell configurations for the two-dimensional metric and scalar field correspond to genuine $d$-dimensional gravitational vacuum solutions. We discuss separately the two-dimensional Horndeski theories which can arise from the reduction of $d$-dimensional generally covariant gravitational actions built only from curvature invariants without covariant derivatives and possessing second-order equations of motion on $2 + (d-2)$ warped-product"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We demonstrate that generic two-dimensional Horndeski theories can arise from the reduction of pure gravities in d ≥ 4 dimensions, and therefore generic onshell configurations for the two-dimensional metric and scalar field correspond to genuine d-dimensional gravitational vacuum solutions.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The reduction is performed on 2+(d-2) warped-product backgrounds and the higher-dimensional action is assumed to produce second-order equations of motion when restricted to such backgrounds; if this restriction does not hold for the full theory or if the warping ansatz misses relevant solutions, the correspondence between 2D onshell configurations and d-dimensional vacuum solutions fails.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Generic 2D Horndeski theories arise from dimensional reduction of d≥4 gravities, yielding a Birkhoff theorem for quasi-topological gravities where static spherically symmetric solutions satisfy g_tt g_rr = -1 and are determined algebraically.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Reductions of pure gravities in d ≥ 4 dimensions yield all generic two-dimensional Horndeski theories.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b948f2bef2506c34901c8dc797c18769f0ff22af4f8ff72246773d95ba62aa20"},"source":{"id":"2603.06786","kind":"arxiv","version":3},"verdict":{"id":"c758a016-0ac6-4f76-a058-bf1934b6be2b","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T14:42:40.564279Z","strongest_claim":"We demonstrate that generic two-dimensional Horndeski theories can arise from the reduction of pure gravities in d ≥ 4 dimensions, and therefore generic onshell configurations for the two-dimensional metric and scalar field correspond to genuine d-dimensional gravitational vacuum solutions.","one_line_summary":"Generic 2D Horndeski theories arise from dimensional reduction of d≥4 gravities, yielding a Birkhoff theorem for quasi-topological gravities where static spherically symmetric solutions satisfy g_tt g_rr = -1 and are determined algebraically.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The reduction is performed on 2+(d-2) warped-product backgrounds and the higher-dimensional action is assumed to produce second-order equations of motion when restricted to such backgrounds; if this restriction does not hold for the full theory or if the warping ansatz misses relevant solutions, the correspondence between 2D onshell configurations and d-dimensional vacuum solutions fails.","pith_extraction_headline":"Reductions of pure gravities in d ≥ 4 dimensions yield all generic two-dimensional Horndeski theories."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.06786/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"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"}