{"paper":{"title":"The 4d superconformal index near roots of unity and 3d Chern-Simons theory","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Arash Arabi Ardehali, Sameer Murthy","submitted_at":"2021-04-05T17:59:12Z","abstract_excerpt":"We consider the $S^3\\times S^1$ superconformal index $\\mathcal{I}(\\tau)$ of 4d $\\mathcal{N}=1$ gauge theories. The Hamiltonian index is defined in a standard manner as the Witten index with a chemical potential $\\tau$ coupled to a combination of angular momenta on $S^3$ and the $U(1)$ R-charge. We develop the all-order asymptotic expansion of the index as $q = e^{2 \\pi i \\tau}$ approaches a root of unity, i.e. as $\\widetilde \\tau \\equiv m \\tau + n \\to 0$, with $m,n$ relatively prime integers. The asymptotic expansion of $\\log\\mathcal{I}(\\tau)$ has terms of the form $\\widetilde \\tau^k$, $k = -2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.02051","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/2104.02051/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"}