{"paper":{"title":"Asymptotics of complex $b$-$6j$ symbols","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math.GT","math.MP"],"primary_cat":"math-ph","authors_text":"Tian Yang, Yunpeng Meng","submitted_at":"2026-06-02T13:43:21Z","abstract_excerpt":"We study the $b$-$6j$ symbols -- an analytic extension of the $6j$-symbols for the principal series of the modular double of $\\mathrm U_q\\mathfrak{sl}(2;\\mathbb R)$ -- with complex index $b,$ refereed to as the \\emph{complex $b$-$6j$ symbols}. Then we relate their asymptotics, when the six parameters scale according to the dihedral angles of a hyperideal hyperbolic tetrahedron, to the volume and the determinant of the Gram matrix of the tetrahedron. In the case $\\arg b=\\pm \\frac{\\pi}{4},$ we believe that this work is closely related to the complex Liouville string\\,\\cite{CEMR}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03653","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/2606.03653/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"}