{"paper":{"title":"Scaling dimensions of Coulomb branch operators of 4d N=2 superconformal field theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Mario Martone, Philip C. Argyres","submitted_at":"2018-01-19T19:09:46Z","abstract_excerpt":"Under reasonable assumptions about the complex structure of the set of singularities on the Coulomb branch of $\\mathcal N=2$ superconformal field theories, we present a relatively simple and elementary argument showing that the scaling dimension, $\\Delta$, of a Coulomb branch operator of a rank $r$ theory is allowed to take values in a finite set of rational numbers$\\Delta\\in \\big[\\frac{n}{m}\\big|n,m\\in\\mathbb N, 0<m\\le n, gcd(n,m)=1,\\ \\varphi(n)\\le2r\\big]$ where $\\varphi(n)$ is the Euler totient function. The maximal dimension grows superlinearly with rank as $\\Delta_\\text{max} \\sim r \\ln\\ln "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06554","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"}