{"paper":{"title":"Existence of mixed type solutions in the Chern-Simons gauge theory of rank two in $\\mathbb{R}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chang-shou Lin, Kwangseok Choe, Namkwon Kim, Youngae Lee","submitted_at":"2017-06-16T15:33:45Z","abstract_excerpt":"We consider the Chern-Simons gauge theory of rank $2$ such as $SU(3)$, $SO(5)$, and $G_2$ Chern-Simons model in $\\mathbb{R}^2$. There may exist three types of solutions in these theories, that is, topological, nontopological, and mixed type solutions. Among others, mixed type solutions can only exist in non-Abelian Chern-Simons models. We show the existence of mixed type solutions with an arbitrary configuration of vortex points which has been a long-standing open problem. To show it, as the first step, we need to find when a priori bound would fail. For the purpose, we shall find partially bl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05319","kind":"arxiv","version":1},"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"}