{"paper":{"title":"The large-$N$ Yang--Mills $\\Lambda$-parameter from step scaling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-lat","authors_text":"Andrea Giorgieri, Claudio Bonanno, Jorge Luis Dasilva Gol\\'an, Margarita Garc\\'ia P\\'erez","submitted_at":"2026-07-08T09:11:10Z","abstract_excerpt":"We use the step-scaling method and results obtained at $N = 3, 5$ and $8$ to determine the $N$-dependence of the dynamically generated scale $\\Lambda$ of $\\mathrm{SU}(N)$ Yang--Mills theories. We implement the step-scaling method in a suitable finite-volume renormalization scheme based on twisted boundary conditions, introduced to effectively achieve large-$N$ volume independence, and on a coupling defined through the gradient flow. In the $\\overline{\\mathrm{MS}}$ scheme, we obtain the following values in terms of the gradient flow scale $t_0$: $\\sqrt{8t_0}\\Lambda_{\\scriptscriptstyle{\\overline"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07176","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.07176/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}