Generalized global symmetries

By D. Gaiotto, A. Kapustin, N. Seiberg, Brian Willett. Journal of High Energy Physics, 2014

1,443 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0a08701ddf1afd62739abc8f046af1acd13bdf1d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. E. Witten
2. D. Gaiotto
3. F. Benini
4. Clay Córdova
5. N. Seiberg
6. Po-Shen Hsin
7. T. Dumitrescu
8. Yuji Tachikawa

In Nuclear and High Energy Physics

1. N. Seiberg
2. Yuji Tachikawa
3. F. Benini
4. Clay Córdova
5. D. Gaiotto
6. E. Witten
7. T. Dumitrescu
8. Z. Komargodski

In Statistical and Nonlinear Physics

1. E. Witten
2. F. Benini
3. N. Seiberg
4. D. Gaiotto
5. Clay Córdova
6. Yuji Tachikawa
7. T. Dumitrescu
8. Po-Shen Hsin

Citations in the corpus

• Generalized Symmetries in Condensed Matter (2022, neutral): “But this is a description of the spontaneous breaking of a higher-form symmetry (16, 25): the generators of the broken part of the higher-form symmetry commute with the Hamiltonian (at least at low energies) and act nontrivially on the groundstates 6 .”
• Chern-Simons-matter dualities with SO and USp gauge groups (2016, background): “In the corresponding 3d CS theory, B(G) appears as a one-form symmetry [37] generated by the lines σi.”
• The Swampland: Introduction and Review (2019, background): “obal symmetries only requires a single charged state, but if we extend it to discrete generalized global symmetries then we require all possible charges in order to break also any discrete symmetries [29]. This is also related to the point that the 7In terms of de Rham cohomology, the dierence betwe”
• Notes on generalized global symmetries in QFT (2015, methodology): “The purpose of this paper is to merely to link the recent work [1] to other work on 2-groups, to review a few highlights, and to provide a few hopefully new results, proposals, and applications.”
• A general proof of the quantum null energy condition (2017, background): “living at @A. In particular the position of branch cut on the replicated manifold becomes irrelevant. This twist operator carries a Ze ncharge, corresponding to a d 2 form generalized global symmetry [100], which arrises when we gauge the original (0-form) replica symmetry. The twist operators are s”
• Universal Non‐Invertible Symmetries (2022, methodology): “1 Revisiting SPT Phases Protected by 0-Form Symmetry We begin by describing a 2d SPT phase protected by abelian Γ 0-form symmetry in a slightly non-traditional language following [12].”
• On the Defect Group of a 6D SCFT (2015, background): “[16, 21, 6]).”
• Lectures on the Swampland Program in String Compactifications (2021, background): “These are generalizations of global symmetries whose charged operators are supported on p-dimensional manifolds [8].”
• Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions (2022, methodology): “The modern characterization of a global symmetry is in terms of its conserved charge or symmetry operator, rather than any specific realization by Lagrangians and fields [1].”
• Theta, time reversal and temperature (2017, methodology): “their expectation values have an area law), the 1-form ZN center symmetry is unbroken [19].”
• Comments on one-form global symmetries and their gauging in 3d and 4d (2018, methodology): “a lot of freedom in adding boundary degrees of freedom. Our main tool for analyzing the system is its ZN one-form global symmetry. Related to this symmetry is an integer label pwith p˘p+ 2Nand pNeven [4,1]. Furthermore, we have an identication in labeling the theories [4,1,2] (;p) ˘(+ 2ˇk;p+ k(N 1))”
• Strong-to-Weak Spontaneous Symmetry Breaking in Mixed Quantum States (2024, neutral): “Strong-to-weak SSB of higher-form symmetry: A topologically ordered state can be understood as the spontaneous symmetry breaking of some higher-form symmetry [45, 46].”
• Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond (2022, background): “For an exposition of this perspective, see for instance [21] and references therein.”
• On finite symmetries and their gauging in two dimensions (2017, background): “Our investigation starts from a related but different question: can it be generalized to non-Abelian finite groups? The answer is again yes [3], and it again requires a generalization of the concept of symmetries, but in a direction different from that of [2].”
• Hierarchy of Topological Order From Finite-Depth Unitaries, Measurement, and Feedforward (2022, background): “Since these defects correspond to charges of 1-form symmetries [99], if they occur as measurement outcomes, they would come from a KW map that gauges a 1-form symmetry, which physically corresponds to anyon condensation.”
• Dai-Freed anomalies in particle physics (2018, background): “69) means coupling to the topological field theory which describes the gauging of a Zn (d− 2) generalized global symmetry [102].”
• Comments on global symmetries, anomalies, and duality in (2 + 1)d (2017, background): “As in [51,52], these can be represented by a two-form field B with a (3+1)d coupling B ∧ B.”