{"paper":{"title":"Modular symmetry by orbifolding magnetized $T^2\\times T^2$: realization of double cover of $\\Gamma_N$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"hep-th","authors_text":"Hajime Otsuka, Hikaru Uchida, Shintaro Takada, Shota Kikuchi, Tatsuo Kobayashi","submitted_at":"2020-07-13T04:55:20Z","abstract_excerpt":"We study the modular symmetry of zero-modes on $T_1^2 \\times T_2^2$ and orbifold compactifications with magnetic fluxes, $M_1,M_2$, where modulus parameters are identified. This identification breaks the modular symmetry of $T^2_1 \\times T^2_2$, $SL(2,\\mathbb{Z})_1 \\times SL(2,\\mathbb{Z})_2$ to $SL(2,\\mathbb{Z})\\equiv\\Gamma$. Each of the wavefunctions on $T^2_1 \\times T^2_2$ and orbifolds behaves as the modular forms of weight 1 for the principal congruence subgroup $\\Gamma$($N$), $N$ being 2 times the least common multiple of $M_1$ and $M_2$. Then, zero-modes transform each other under the mo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.06188","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/2007.06188/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"}