{"paper":{"title":"Holographic RG flows on curved manifolds and the $F$-theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Elias Kiritsis, Francesco Nitti, Jewel Kumar Ghosh, Lukas T. Witkowski","submitted_at":"2018-10-29T18:00:32Z","abstract_excerpt":"We study $F$-functions in the context of field theories on $S^3$ using gauge-gravity duality, with the radius of $S^3$ playing the role of RG scale. We show that the on-shell action, evaluated over a set of holographic RG flow solutions, can be used to define good $F$-functions, which decrease monotonically along the RG flow from the UV to the IR for a wide range of examples. If the operator perturbing the UV CFT has dimension $\\Delta > 3/2$ these $F$-functions correspond to an appropriately renormalized free energy. If instead the perturbing operator has dimension $\\Delta < 3/2$ it is the qua"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12318","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}