{"paper":{"title":"Exact SL(2,Z)-Structure of Lattice Maxwell Theory with $\\theta$-term in Modified Villain Formulation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Lattice Maxwell theory with theta term exhibits exact SL(2,Z) duality in the modified Villain formulation.","cross_cats":["cond-mat.str-el","hep-th"],"primary_cat":"hep-lat","authors_text":"Shoto Aoki, Toshinari Takemoto, Yoshio Kikukawa","submitted_at":"2026-04-09T20:00:03Z","abstract_excerpt":"We study the duality of lattice Maxwell theory in the modified Villain formulation, employing an ultra-local action with a theta term. Although this action is known to become non ultra-local through the Poisson resummation formula, we show that this non ultra-locality can be removed by incorporating a non-local transformation procedure into the definition of the S-transformation. As a result, the ultra-local action with a theta term exhibits an exact SL(2,Z)-duality. We further analyze the SL(2,Z)-structure of Wilson and 't Hooft loops, demonstrating that they transform properly up to a nontri"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"As a result, the ultra-local action with a theta term exhibits an exact SL(2,Z)-duality. We further analyze the SL(2,Z)-structure of Wilson and 't Hooft loops, demonstrating that they transform properly up to a nontrivial phase factor arising from the nontrivial self-linking of the loops.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the non-local transformation procedure added to the S-transformation removes non ultra-locality from the Poisson resummation without introducing inconsistencies or changing the physical content of the duality.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The ultra-local modified Villain action for lattice Maxwell theory with theta term has exact SL(2,Z) duality, with Wilson and 't Hooft loops transforming up to a phase from self-linking.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Lattice Maxwell theory with theta term exhibits exact SL(2,Z) duality in the modified Villain formulation.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"4289384dbe6ee16cb2eb1dcda5471a9aa4887b32ba070f97c9858af916e1756a"},"source":{"id":"2604.08736","kind":"arxiv","version":3},"verdict":{"id":"d14ba3cf-22b4-4c0f-b3e7-7d188f93a87c","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T16:51:09.699932Z","strongest_claim":"As a result, the ultra-local action with a theta term exhibits an exact SL(2,Z)-duality. We further analyze the SL(2,Z)-structure of Wilson and 't Hooft loops, demonstrating that they transform properly up to a nontrivial phase factor arising from the nontrivial self-linking of the loops.","one_line_summary":"The ultra-local modified Villain action for lattice Maxwell theory with theta term has exact SL(2,Z) duality, with Wilson and 't Hooft loops transforming up to a phase from self-linking.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the non-local transformation procedure added to the S-transformation removes non ultra-locality from the Poisson resummation without introducing inconsistencies or changing the physical content of the duality.","pith_extraction_headline":"Lattice Maxwell theory with theta term exhibits exact SL(2,Z) duality in the modified Villain formulation."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.08736/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"}