{"paper":{"title":"SYM on Quotients of Spheres and Complex Projective Spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Jim Lundin, Lorenzo Ruggeri","submitted_at":"2021-10-25T16:00:00Z","abstract_excerpt":"We introduce a generic procedure to reduce a supersymmetric Yang-Mills (SYM) theory along the Hopf fiber of squashed $S^{2r-1}$ with $U(1)^r$ isometry, down to the $\\mathbb{CP}^{r-1}$ base. This amounts to fixing a Killing vector $v$ generating a $U(1)\\subset U(1)^r$ rotation and dimensionally reducing either along $v$ or along another direction contained in $U(1)^r$. To perform such reduction we introduce a $\\mathbb{Z}_p$ quotient freely acting along one of the two fibers. For fixed $p$ the resulting manifolds $S^{2r-1}/\\mathbb{Z}_p\\equiv L^{2r-1}(p,\\pm 1)$ are a higher dimensional generaliza"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.13065","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/2110.13065/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"}