{"paper":{"title":"Symmetry protection of critical phases and global anomaly in $1+1$ dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","hep-th"],"primary_cat":"cond-mat.stat-mech","authors_text":"Masaki Oshikawa, Shunsuke C. Furuya","submitted_at":"2015-03-25T06:31:51Z","abstract_excerpt":"We derive a selection rule among the $(1+1)$-dimensional SU(2) Wess-Zumino-Witten theories, based on the global anomaly of the discrete $\\mathbb{Z}_2$ symmetry found by Gepner and Witten. In the presence of both the SU(2) and $\\mathbb{Z}_2$ symmetries, a renormalization-group flow is possible between level-$k$ and level-$k'$ Wess-Zumino-Witten theories only if $k\\equiv k' \\mod{2}$. This classifies the Lorentz-invariant, SU(2)-symmetric critical behavior into two \"symmetry-protected\" categories corresponding to even and odd levels,restricting possible gapless critical behavior of translation-in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07292","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}