{"paper":{"title":"Conformal invariance from scale invariance in non-linear sigma models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Yu Nakayama","submitted_at":"2020-06-09T06:34:25Z","abstract_excerpt":"There exists a certain argument that in even dimensions, scale invariant quantum field theories are conformal invariant. We may try to extend the argument in $2n + \\epsilon$ dimensions, but the naive extension has a small loophole, which indeed shows an obstruction in non-linear sigma models in $2+\\epsilon$ dimensions. Even though it could have failed due to the loophole, we show that scale invariance does imply conformal invariance of non-linear sigma models in $2+\\epsilon$ dimension from the seminal work by Perelman on the Ricci flow."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.05070","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.05070/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"}