{"paper":{"title":"Equivariant Verlinde algebra from superconformal index and Argyres-Seiberg duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AT","math.QA","math.RT"],"primary_cat":"hep-th","authors_text":"Du Pei, Ke Ye, Sergei Gukov, WenBin Yan","submitted_at":"2016-05-20T20:21:04Z","abstract_excerpt":"In this paper, we show the equivalence between two seemingly distinct 2d TQFTs: one comes from the \"Coulomb branch index\" of the class S theory $T[\\Sigma,G]$ on $L(k,1) \\times S^1$, the other is the $^LG$ \"equivariant Verlinde formula\", or equivalently partition function of $^LG_{\\mathbb{C}}$ complex Chern-Simons theory on $\\Sigma\\times S^1$. We first derive this equivalence using the M-theory geometry and show that the gauge groups appearing on the two sides are naturally $G$ and its Langlands dual $^LG$. When $G$ is not simply-connected, we provide a recipe of computing the index of $T[\\Sigm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06528","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":""},"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"}