Generalized global symmetries
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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 sub-group). 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.
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The record
- Venue
- Journal of High Energy Physics
- Topic
- Black Holes and Theoretical Physics
- Field
- Physics and Astronomy
- Canadian institutions
- Perimeter Institute
- Funders
- Institut Périmètre de physique théoriqueIndustry CanadaU.S. Department of EnergyMinistero dello Sviluppo EconomicoUnited States-Israel Binational Science FoundationGovernment of Canada
- Keywords
- Homogeneous spaceAnomaly (physics)Symmetry (geometry)Global symmetryPhysicsGroup (periodic table)Theoretical physicsSpacetime symmetriesSymmetry groupSurface (topology)Space (punctuation)Dimension (graph theory)Mathematical physicsMathematicsQuantum mechanicsPure mathematicsSpontaneous symmetry breakingSymmetry breakingGeometryComputer science
- Has abstract in OpenAlex
- yes