{"paper":{"title":"Affine 7-brane Backgrounds and Five-Dimensional $E_N$ Theories on $S^1$","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Sung-Kil Yang, Yasuhiko Yamada","submitted_at":"1999-07-16T00:42:45Z","abstract_excerpt":"Elliptic curves for the 7-brane configurations realizing the affine Lie algebras $\\wh E_n$ $(1 \\leq n \\leq 8)$ and $\\wh{\\wt E}_n$ $(n=0,1)$ are systematically derived from the cubic equation for a rational elliptic surface. It is then shown that the $\\wh E_n$ 7-branes describe the discriminant locus of the elliptic curves for five-dimensional (5D) N=1 $E_n$ theories compactified on a circle. This is in accordance with a recent construction of 5D N=1 $E_n$ theories on the IIB 5-brane web with 7-branes, and indicates the validity of the D3 probe picture for 5D $E_n$ theories on $\\bR^4 \\times S^1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9907134","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":""},"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"}