{"paper":{"title":"$\\theta=\\pi$ in $SU(N)/\\mathbb{Z}_N$ gauge theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-lat","hep-ph"],"primary_cat":"hep-th","authors_text":"Norikazu Yamada, Ryuichiro Kitano, Takao Suyama","submitted_at":"2017-09-13T09:53:37Z","abstract_excerpt":"In $SU(N)$ gauge theory, it is argued recently that there exists a \"mixed anomaly\" between the CP symmetry and the 1-form $\\mathbb{Z}_N$ symmetry at $\\theta=\\pi$, and the anomaly matching requires CP to be spontaneously broken at $\\theta=\\pi$ if the system is in the confining phase. In this paper, we elaborate on this discussion by examining the large volume behavior of the partition functions of the $SU(N)/\\mathbb{Z}_N$ theory on $T^4$ a la 't Hooft. The periodicity of the partition function in $\\theta$, which is not $2\\pi$ due to fractional instanton numbers, suggests the presence of a phase"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04225","kind":"arxiv","version":2},"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"}