{"paper":{"title":"Duality symmetry, zero energy modes and boundary spectrum of the sine-Gordon/massive Thirring model","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el"],"primary_cat":"hep-th","authors_text":"Ari Mizel, Parameshwar R. Pasnoori, Patrick Azaria","submitted_at":"2025-03-18T23:04:20Z","abstract_excerpt":"We solve the one-dimensional massive Thirring model, which is equivalent to the one-dimensional sine-Gordon model, with two types of Dirchlet boundary conditions: open boundary conditions (OBC) and twisted open boundary conditions ($\\widehat{\\text{OBC}}$). The system exhibits a duality symmetry which relates models with opposite bare mass parameters and boundary conditions, i.e: $m_0 \\leftrightarrow - m_0$, $\\text{OBC}\\leftrightarrow\\widehat{\\text{OBC}}$. For $m_0<0$ and OBC, the system is in a trivial phase whose ground state is unique, as in the case of periodic boundary conditions. In contr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.14776","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/2503.14776/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"}