{"work":{"id":"f2e472ff-a033-449e-9266-1a04fef855c0","openalex_id":null,"doi":null,"arxiv_id":"1412.5148","raw_key":null,"title":"Generalized Global Symmetries","authors":null,"authors_text":"Davide Gaiotto, Anton Kapustin, Nathan Seiberg, Brian Willett","year":2014,"venue":"hep-th","abstract":"A $q$-form global symmetry is a global symmetry for which the charged operators are of space-time dimension $q$; e.g. Wilson lines, surface defects, etc., and the charged excitations have $q$ spatial dimensions; e.g. strings, membranes, etc. Many of the properties of ordinary global symmetries ($q$=0) apply here. They lead to Ward identities and hence to selection rules on amplitudes. Such global symmetries can be coupled to classical background fields and they can be gauged by summing over these classical fields. These generalized global symmetries can be spontaneously broken (either completely or to a subgroup). They can also have 't Hooft anomalies, which prevent us from gauging them, but lead to 't Hooft anomaly matching conditions. Such anomalies can also lead to anomaly inflow on various defects and exotic Symmetry Protected Topological phases. Our analysis of these symmetries gives a new unified perspective of many known phenomena and uncovers new results.","external_url":"https://arxiv.org/abs/1412.5148","cited_by_count":null,"metadata_source":"pith","metadata_fetched_at":"2026-05-25T05:20:24.653279+00:00","pith_arxiv_id":"1412.5148","created_at":"2026-05-09T06:40:39.647341+00:00","updated_at":"2026-06-05T21:23:00.469572+00:00","title_quality_ok":false,"display_title":"Generalized Global Symmetries","render_title":"Generalized Global Symmetries"},"hub":{"state":{"work_id":"f2e472ff-a033-449e-9266-1a04fef855c0","tier":"hub","tier_reason":"10+ Pith inbound or 1,000+ external citations","pith_inbound_count":74,"external_cited_by_count":null,"distinct_field_count":7,"first_pith_cited_at":"2021-11-01T18:00:00+00:00","last_pith_cited_at":"2026-05-21T21:26:52+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":"2026-06-08T20:43:57.694951+00:00","tier_text":"hub"},"tier":"hub","role_counts":[{"context_role":"background","n":40},{"context_role":"method","n":3}],"polarity_counts":[{"context_polarity":"background","n":40},{"context_polarity":"use_method","n":3}],"runs":{"context_extract":{"job_type":"context_extract","status":"succeeded","result":{"enqueued_papers":25},"error":null,"updated_at":"2026-05-24T07:45:11.315038+00:00"},"graph_features":{"job_type":"graph_features","status":"succeeded","result":{"co_cited":[{"title":"ICTP Lectures on (Non-)Invertible Generalized Symmetries","work_id":"63ae42b5-8b0a-40e3-9f9d-50a57be4043c","shared_citers":32},{"title":"What’s Done Cannot Be Undone: TASI Lectures on Non-Invertible Sym- metries","work_id":"3e4726a4-120f-43de-89d7-81589b94d413","shared_citers":29},{"title":"Lectures on Generalized Symmetries","work_id":"aac2c85e-c2a1-4c51-a019-7fa153696908","shared_citers":24},{"title":"Apruzzi, F","work_id":"d25fe5fa-24e3-4c1c-9026-c08b9409c00b","shared_citers":22},{"title":"Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond","work_id":"3e8f57bb-7d9b-476b-86ff-1faf57e92e26","shared_citers":21},{"title":"Topological Defect Lines and Renormalization Group Flows in Two Dimensions","work_id":"5f511e19-37c3-4834-afe2-0bcfab6aa73d","shared_citers":21},{"title":"Topological symmetry in quantum field theory","work_id":"87a0ca97-a68d-4f30-a895-5965f1dd1d5a","shared_citers":21},{"title":"McGreevy, Generalized Symmetries in Condensed Matter, Annual Review of Condensed Matter Physics14, 57 (2023)","work_id":"25a404fd-1148-4d5f-af03-4c50e23ed074","shared_citers":19},{"title":"Kaidi, K","work_id":"7fee217c-46f6-4c4b-9670-52c8d43f8768","shared_citers":18},{"title":"Non invertible duality defects in 3+1 dimensions,","work_id":"020859d9-308b-430d-844c-e72ea4f0d492","shared_citers":18},{"title":"Roumpedakis, S","work_id":"803bdc04-fe38-4991-8aa2-5700a6e4a188","shared_citers":18},{"title":"Introduction to Generalized Global Symmetries in QFT and Particle Physics","work_id":"5e9b01a1-6944-42e6-88fe-a6e41b2b8532","shared_citers":17},{"title":"Bhardwaj and Y","work_id":"db1acc3b-e257-4442-8c91-9ee1ac627dc1","shared_citers":16},{"title":"Gaiotto and J","work_id":"4ff43ce9-35c9-4295-8721-37c83aa76c13","shared_citers":16},{"title":"Kapustin and N","work_id":"3bbce13f-936f-4ad2-9dfe-0081b090e265","shared_citers":16},{"title":"On gauging finite subgroups","work_id":"61e0feb2-3152-479a-ae50-298fb1290de7","shared_citers":16},{"title":"Fr¨ ohlich, J","work_id":"308c0a79-7c28-4d91-9b36-ea2dea6b6c2d","shared_citers":15},{"title":"Fuchs, I","work_id":"0f0e1d88-f90f-464d-ba0e-03f32c85b4f4","shared_citers":15},{"title":"Fusion category symmetry. 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The resulting phase change could be interpreted as a holonomy in polarization space arising from interface-induced matching of electromagnetic polarization states across an in- terface separating topologically distinct dark-sector vacua. The structure of the interface is constrained by an emergent 1-form symmetry [ 18], which protects the allowed phase jump and renders it insensitive to local details of the interpolation between vacua [ 19, 20]. Con- sequently, in the absence of adiabatically varying light axions, polarization rotation occurs only at localized vacuum interfaces, and its magnitude is determined by global topological data rather than by local dynamics or the cosmological history between crossings.","citing_arxiv_id":"2605.11065"},{"n":1,"role":"method","polarity":"use_method","paper_title":"de Sitter Vacua & pUniverses","primary_cat":"hep-th","context_text":"p 1-form global symmetry, acting on the Wilson lines as Z(1) p : ˆWj[C]→e 2πij p ˆWj[C] (3.1.11) As it turns out, as a consequence of the chiral anomaly (3.1.4), theZ (0) p chiral symmetry and the Z(1) p 1-form symmetry participate in aZ p-valued mixed 't Hooft anomaly. This anomaly is of the same type as the one described by (2.1.6) for the BF theory in the previous section. From the perspective of [37], the global symmetries described above imply the existence of a discrete set of topological operators. TheZ (0) p chiral symmetry will be implemented by topological-line operators ˆLn[C],n∈0,1, . . . p−1, extended over a closed curveC, while theZ (1) p 1-form symmetry will be generated by topological-local operators that we denote by ˆUm(x),m∈0,1, .","citing_arxiv_id":"2605.02883"},{"n":1,"role":"method","polarity":"use_method","paper_title":"Lectures on Generalized Symmetries","primary_cat":"hep-th","context_text":"metriesingeometricengineeringconstructionsofquantumfieldtheoriesviastringtheory, and the study of higher-form symmetries using holographic duality. 2 Introduction to Higher-Form Symmetries The aim of this section is to introducep-form symmetries. These symmetries generalize the usual global symmetries, which in this language are referred to as 0-form symmetries. We will follow the seminal work [4], though this is not to say that this was the first work discussing such ideas. In fact, many of the ideas involved can be traced to works by various communities in late 1980s and early 1990s in the study of non-perturbative aspects of gauge theories, discrete gauge theories, rational CFTs and Chern-Simons theories. 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Haegeman, and F. Verstraete,Mapping topological to conformal field theories through strange correlators, Phys. Rev. Lett.121(2018) 177203, arXiv:1801.05959 [quant-ph]. [42] K. Inamura,Topological field theories and symmetry protected topological phases with fusion category symmetries,Journal of High Energy Physics202","claim_type":"background","confidence":0.9,"evidence_strength":"citation_context"},{"claim_text":"Alternatively, it is sourced by a localizedG-flux (fractional, in the discrete case). 1 Introduction The space of defects in a quantum system has been the subject of intense recent study: defects arise naturally as impurities in condensed-matter setups, and serve as probes of strongly coupled bulk dy- namics. 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