Generalized Global Symmetries

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.

49 pages plus appendices. v2: references added

References in corpus (11)

• Symmetries and Strings in Field Theory and Gravity
• Duality and defects in rational conformal field theory
• Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology
• The Uncertainty of Fluxes
• Heisenberg Groups and Noncommutative Fluxes
• Comments on the Fayet-Iliopoulos Term in Field Theory and Supergravity
• Anomalies of discrete symmetries in various dimensions and group cohomology
• Short-range entanglement and invertible field theories
• Discrete torsion defects
• Topological Model for Domain Walls in (Super-)Yang-Mills Theories
• On Orbits of the Ring $Z_n^m$ under the Action of the Group $SL(m,Z_n)$

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• Ramond-Ramond couplings of D-branes
• OPE of the stress tensors and surface operators