{"paper":{"title":"Relative scale separation in orbifolds of $S^2$ and $S^5$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Dimitrios Tsimpis","submitted_at":"2022-01-26T13:06:15Z","abstract_excerpt":"In orbifold vacua containing an $S^q/\\Gamma$ factor, we compute the relative order of scale separation, $r$, defined as the ratio of the eigenvalue of the lowest-lying $\\Gamma$-invariant state of the scalar Laplacian on $S^q$, to the eigenvalue of the lowest-lying state. For $q=2$ and $\\Gamma$ finite subgroup of $SO(3)$, or $q=5$ and $\\Gamma$ finite subgroup of $SU(3)$, the maximal relative order of scale separation that can be achieved is $r=21$ or $r=12$, respectively. For smooth $S^5$ orbifolds, the maximal relative scale separation is $r=4.2$. Methods from invariant theory are very efficie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.10916","kind":"arxiv","version":3},"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/2201.10916/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"}