{"paper":{"title":"Analytic continuation of dimensions in supersymmetric localization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Anastasios Gorantis, Joseph A. Minahan, Usman Naseer","submitted_at":"2017-11-15T17:05:07Z","abstract_excerpt":"We compute the perturbative partition functions for gauge theories with eight supersymmetries on spheres of dimension $d\\le5$, proving a conjecture by the second author. We apply similar methods to gauge theories with four supersymmetries on spheres with $d\\le3$. The results are valid for non-integer $d$ as well. We further propose an analytic continuation from $d=3$ to $d=4$ that gives the perturbative partition function for an $\\mathcal{N}=1$ gauge theory. The results are consistent with the free multiplets and the one-loop $\\beta$-functions for general $\\mathcal{N}=1$ gauge theories. We als"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05669","kind":"arxiv","version":4},"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"}