{"paper":{"title":"The Cost of Seven-brane Gauge Symmetry in a Quadrillion F-theory Compactifications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"James Halverson, Jiahua Tian","submitted_at":"2016-10-27T16:16:46Z","abstract_excerpt":"We study seven-branes in $O(10^{15})$ four-dimensional F-theory compactifications where seven-brane moduli must be tuned in order to achieve non-abelian gauge symmetry. The associated compact spaces $B$ are the set of all smooth weak Fano toric threefolds. By a study of fine star regular triangulations of three dimensional reflexive polytopes, the number of such spaces is estimated to be $5.8\\times 10^{14}\\lesssim N_\\text{bases}\\lesssim 1.8\\times 10^{17}$. Typically hundreds or thousands of moduli must be tuned to achieve symmetry for $h^{11}(B)<10$, but the average number drops sharply into t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08864","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"}