{"paper":{"title":"Direct Monte Carlo Computation of the 't~Hooft Partition Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-lat","authors_text":"Hiroshi Suzuki, Okuto Morikawa","submitted_at":"2025-01-13T03:48:11Z","abstract_excerpt":"The 't~Hooft partition function~$\\mathcal{Z}_{\\text{tH}}[E;B]$ of an $SU(N)$ gauge theory with the $\\mathbb{Z}_N$ 1-form symmetry is defined as the Fourier transform of the partition function~$\\mathcal{Z}[B]$ with respect to the spatial-temporal components of the 't~Hooft flux~$B$. Its large volume behavior detects the quantum phase of the system. When the integrand of the functional integral is real-positive, the latter partition function~$\\mathcal{Z}[B]$ can be numerically computed by a Monte Carlo simulation of the $SU(N)/\\mathbb{Z}_N$ gauge theory, just by counting the number of configurat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.07042","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.07042/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"}