Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond

Abstract

Symmetry plays a central role in quantum field theory. Recent developments include symmetries that act on defects and other subsystems, and symmetries that are categorical rather than group-like. These generalized notions of symmetry allow for new kinds of anomalies that constrain dynamics. We review some transformative instances of these novel aspects of symmetry in quantum field theory, and give a broad-brush overview of recent applications.

Contribution to 2022 Snowmass Summer Study. 10 pages + bibliography

Cited by in corpus (43)

• The Branes Behind Generalized Symmetry Operators
• Majorana chain and Ising model -- (non-invertible) translations, anomalies, and emanant symmetries
• Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space
• Anomalies and Symmetry Fractionalization
• An Introduction to Higher-Form Symmetries
• Mixed Anomalies, Two-groups, Non-Invertible Symmetries, and 3d Superconformal Indices
• Codimension-2 defects and higher symmetries in (3+1)D topological phases
• Subsystem Non-Invertible Symmetry Operators and Defects
• Anomalies of Non-Invertible Symmetries in (3+1)d
• Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries
• Fusion Surface Models: 2+1d Lattice Models from Fusion 2-Categories
• Topological Defect Lines in Two Dimensional Fermionic CFTs
• Topological holography, quantum criticality, and boundary states
• Non-invertible and higher-form symmetries in 2+1d lattice gauge theories
• Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections
• From the XXZ chain to the integrable Rydberg-blockade ladder via non-invertible duality defects
• Intrinsically/Purely Gapless-SPT from Non-Invertible Duality Transformations
• Emergent generalized symmetries in ordered phases and applications to quantum disordering
• Lattice T-duality from non-invertible symmetries in quantum spin chains
• Ideal fracton superfluids
• Composing topological domain walls and anyon mobility
• Realizing triality and $p$-ality by lattice twisted gauging in (1+1)d quantum spin systems
• Fractionalization of Coset Non-Invertible Symmetry and Exotic Hall Conductance
• Fermionic Higher-form Symmetries
• Higher-group symmetry of (3+1)D fermionic ${\mathbb{Z}}_2$ gauge theory: logical CCZ, CS, and T gates from higher symmetry
• Fermionic Non-Invertible Symmetries in (1+1)d: Gapped and Gapless Phases, Transitions, and Symmetry TFTs
• Gauging non-invertible symmetries on the lattice
• Topologically stable ergodicity breaking from emergent higher-form symmetries in generalized quantum loop models
• 3d $\mathcal{N}=4$ mirror symmetry with 1-form symmetry
• Fractons on Graphs and Complexity
• Symmetries and anomalies of Kitaev spin-$S$ models: Identifying symmetry-enforced exotic quantum matter
• Topological Defects in Floquet Circuits
• Higgs-Confinement Transitions in QCD from Symmetry Protected Topological Phases
• Topological aspects of brane fields: solitons and higher-form symmetries
• Subsystem Symmetry Fractionalization and Foliated Field Theory
• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
• Anomaly of $(2+1)$-Dimensional Symmetry-Enriched Topological Order from $(3+1)$-Dimensional Topological Quantum Field Theory
• Non-Invertible Gauss Law and Axions
• Galilei particles revisited
• Intertwined order of generalized global symmetries
• Non-invertible symmetries of two-dimensional Non-Linear Sigma Models
• Higher-form anomalies and state-operator correspondence beyond conformal invariance
• Generalized symmetry enriched criticality in (3+1)d