{"paper":{"title":"Gradient Flows and the Curvature of Theory Space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-ph"],"primary_cat":"hep-th","authors_text":"Andreas Stergiou, William H. Pannell","submitted_at":"2025-02-10T19:00:01Z","abstract_excerpt":"The metric and potential associated with the gradient property of renormalisation group flow in multiscalar models in $d=4-\\varepsilon$ dimensions are studied. The metric is identified with the Zamolodchikov metric of nearly marginal operators on the sphere. An explicit form for the associated Ricci scalar in $d=4-\\varepsilon$ is derived, which shows that the space of multiscalar field theories is curved. The potential is identified with a quantity $\\widetilde{F}$ that was previously proposed as a weakly monotonic function interpolating between the $a$-theorem in four dimensions and the $F$-th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06940","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.06940/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"}