{"work":{"id":"ca081eed-e25c-4a5b-9358-a03dd3686367","openalex_id":null,"doi":null,"arxiv_id":"1812.04716","raw_key":null,"title":"Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d","authors":null,"authors_text":"P","year":2018,"venue":"hep-th","abstract":"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 $\\mathcal{A}^{N,p}$ is a minimal TQFT with the $\\mathbb{Z}_N$ one-form symmetry of label $p$. The parameter $p$ labels the obstruction to gauging the $\\mathbb{Z}_N$ one-form symmetry; i.e.\\ it characterizes the 't Hooft anomaly of the global symmetry. When $p=0$ mod $2N$, the symmetry can be gauged. Otherwise, it cannot be gauged unless we couple the system to a 4d bulk with gauge fields extended to the bulk. This understanding allows us to consider $SU(N)$ and $PSU(N)$ 4d gauge theories. Their dynamics is gapped and it is associated with confinement and oblique confinement -- probe quarks are confined. In the $PSU(N)$ theory the low-energy theory can include a discrete gauge theory. We will study the behavior of the theory with a space-dependent $\\theta$-parameter, which leads to interfaces. Typically, the theory on the interface is not confining. Furthermore, the liberated probe quarks are anyons on the interface. The $PSU(N)$ theory is obtained by gauging the $\\mathbb{Z}_N$ one-form symmetry of the $SU(N)$ theory. Our understanding of the symmetries in 3d TQFTs allows us to describe the interface in the $PSU(N)$ theory.","external_url":"https://arxiv.org/abs/1812.04716","cited_by_count":null,"metadata_source":"pith","metadata_fetched_at":"2026-05-24T09:58:23.282417+00:00","pith_arxiv_id":"1812.04716","created_at":"2026-05-11T12:21:03.875754+00:00","updated_at":"2026-06-05T21:23:00.469572+00:00","title_quality_ok":true,"display_title":"Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d","render_title":"Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d"},"hub":{"state":{"work_id":"ca081eed-e25c-4a5b-9358-a03dd3686367","tier":"hub","tier_reason":"10+ Pith inbound or 1,000+ external citations","pith_inbound_count":16,"external_cited_by_count":null,"distinct_field_count":3,"first_pith_cited_at":"2021-11-01T18:00:00+00:00","last_pith_cited_at":"2026-05-15T18:00:00+00:00","author_build_status":"not_needed","summary_status":"needed","contexts_status":"needed","graph_status":"needed","ask_index_status":"not_needed","reader_status":"not_needed","recognition_status":"not_needed","updated_at":"2026-06-09T15:15:01.692836+00:00","tier_text":"hub"},"tier":"hub","role_counts":[{"context_role":"background","n":10},{"context_role":"other","n":1}],"polarity_counts":[{"context_polarity":"background","n":10},{"context_polarity":"unclear","n":1}],"runs":{},"summary":{},"graph":{},"authors":[]}}