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A 3d topological quantum field theory (TQFT) $\\mathcal{T}$ with such a symmetry has $N$ special lines that generate it. The braiding of these lines and their spins are characterized by a single integer $p$ modulo $2N$. Surprisingly, if $\\gcd(N,p)=1$ the TQFT factorizes $\\mathcal{T}=\\mathcal{T}'\\otimes \\mathcal{A}^{N,p}$. Here $\\mathcal{T}'$ is a decoupled TQFT, whose lines are neutral under the global symmetry and $\\m"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1812.04716","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-12-11T22:04:10Z","cross_cats_sorted":["cond-mat.str-el"],"title_canon_sha256":"506407639fdcfcea3b99cd42727cbe6f0499c4a4c68d09e43be192826b020610","abstract_canon_sha256":"16b167bbd766fce081f21f79aa9692c9f6dc6510898f0b92c43f30b0d206ad00"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:50.423741Z","signature_b64":"zGV9sysQ4NXaOVdKBmOXI/86ynWOtfQjO7uA1V1cgcsGxbil+m/Qq+X8BYUFkyqOynFu5O9P3TDURc7EurABDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ccba03d2fbb4025b1a6e203e532c8505acfa6c4f17bfab07ec76887c94bae773","last_reissued_at":"2026-05-17T23:49:50.423310Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:50.423310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el"],"primary_cat":"hep-th","authors_text":"Ho Tat Lam, Nathan Seiberg, Po-Shen Hsin","submitted_at":"2018-12-11T22:04:10Z","abstract_excerpt":"We study 3d and 4d systems with a one-form global symmetry, explore their consequences, and analyze their gauging. For simplicity, we focus on $\\mathbb{Z}_N$ one-form symmetries. A 3d topological quantum field theory (TQFT) $\\mathcal{T}$ with such a symmetry has $N$ special lines that generate it. The braiding of these lines and their spins are characterized by a single integer $p$ modulo $2N$. Surprisingly, if $\\gcd(N,p)=1$ the TQFT factorizes $\\mathcal{T}=\\mathcal{T}'\\otimes \\mathcal{A}^{N,p}$. Here $\\mathcal{T}'$ is a decoupled TQFT, whose lines are neutral under the global symmetry and 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