{"paper":{"title":"One constant to rule them all","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Symmetry fixes the coupling matrix of N=2 SU(N) theories with 2N hypermultiplets to floor(N/2) constants, one of which is distinguished in S-duality, asymptotics, and instanton recursion.","cross_cats":[],"primary_cat":"hep-th","authors_text":"Aleksei Bykov, Ekaterina Sysoeva","submitted_at":"2025-12-15T22:18:24Z","abstract_excerpt":"We study the coupling matrix of $\\mathcal{N}=2$ $SU(N)$ gauge theories with $2N$ fundamental hypermultiplets in the special vacuum, where a residual $\\mathbb{Z}_N$ symmetry restores nontrivial modular structure. Using symmetry and dimensional arguments, we construct its general form and identify $\\lfloor N/2 \\rfloor$ coupling constants in their most natural basis. We show that in the massless theory these couplings transform independently under $S$-duality and that the bare coupling is a modular function of any of them. One coupling constant, however, plays a distinguished role, emerging in th"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"One coupling constant, however, plays a distinguished role, emerging in the asymptotic regime and in instanton recursion relation. In the massive case, this structure is deformed but the distinguished coupling retains its privileged role.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"Using symmetry and dimensional arguments, we construct its general form and identify floor(N/2) coupling constants in their most natural basis. The assumption that these arguments are sufficient to uniquely fix the form and the natural basis without additional input.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"In these supersymmetric theories, the coupling matrix has floor(N/2) independent constants under S-duality, with one distinguished constant that remains key in asymptotic and instanton regimes.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Symmetry fixes the coupling matrix of N=2 SU(N) theories with 2N hypermultiplets to floor(N/2) constants, one of which is distinguished in S-duality, asymptotics, and instanton recursion.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"dfbc9952274161a25f52f9ed20fdf2bb249a86c07c5aca2bc4a3a223284d54a8"},"source":{"id":"2512.13934","kind":"arxiv","version":2},"verdict":{"id":"2d057f52-639d-4d40-9ba3-521f3f33a150","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T21:28:03.678203Z","strongest_claim":"One coupling constant, however, plays a distinguished role, emerging in the asymptotic regime and in instanton recursion relation. In the massive case, this structure is deformed but the distinguished coupling retains its privileged role.","one_line_summary":"In these supersymmetric theories, the coupling matrix has floor(N/2) independent constants under S-duality, with one distinguished constant that remains key in asymptotic and instanton regimes.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"Using symmetry and dimensional arguments, we construct its general form and identify floor(N/2) coupling constants in their most natural basis. The assumption that these arguments are sufficient to uniquely fix the form and the natural basis without additional input.","pith_extraction_headline":"Symmetry fixes the coupling matrix of N=2 SU(N) theories with 2N hypermultiplets to floor(N/2) constants, one of which is distinguished in S-duality, asymptotics, and instanton recursion."},"references":{"count":10,"sample":[{"doi":"","year":1994,"title":"Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD","work_id":"12360e87-a168-4339-a34a-9e70f6fd477a","ref_index":2,"cited_arxiv_id":"hep-th/9408099","is_internal_anchor":true},{"doi":"","year":2010,"title":"Liouville Correlation Functions from Four-dimensional Gauge Theories","work_id":"6cbe0ec4-3f62-46db-92d7-10ae96169e65","ref_index":3,"cited_arxiv_id":"0906.3219","is_internal_anchor":true},{"doi":"","year":1996,"title":"$N=2$ Super Yang-Mills and Subgroups of $SL(2,Z)$","work_id":"9132ca8c-c031-4f70-8d48-06c0ba7eb40d","ref_index":4,"cited_arxiv_id":"hep-th/9601059","is_internal_anchor":true},{"doi":"","year":2016,"title":"S-duality, triangle groups and modular anomalies in N=2 SQCD","work_id":"5b37f026-1874-49e4-84a9-03e394b11cfa","ref_index":5,"cited_arxiv_id":"1601.01827","is_internal_anchor":true},{"doi":"","year":null,"title":"Aleksei Bykov, Ekaterina Sysoeva, Zamolodchikov recurrence relation and modular properties of effective coupling inN= 2 SQCD, arXiv:2507.20876 [hep-th] 21","work_id":"bef8c6e7-982c-4d0f-99ad-caf6677911a0","ref_index":6,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":10,"snapshot_sha256":"8d08460171b69d8b58a1b53df6462b362567cef44bb386947ff056a9ff2fd10c","internal_anchors":9},"formal_canon":{"evidence_count":2,"snapshot_sha256":"f22b5083a216b996ca54059dc3db1d089036392a894fd6c23ac9d3b7f9c08ad9"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}