On completeness and generalized symmetries in quantum field theory

Abstract

We review a notion of completeness in QFT arising from the analysis of basic properties of the set of operator algebras attached to regions. In words, this completeness asserts that the physical observable algebras produced by local degrees of freedom are the maximal ones compatible with causality. We elaborate on equivalent statements to this completeness principle such as the non-existence of generalized symmetries and the uniqueness of the net of algebras. We clarify that for non-complete theories, the existence of generalized symmetries is unavoidable, and further, that they always come in dual pairs with precisely the same ``size''. Moreover, the dual symmetries are always broken together, be it explicitly or effectively. Finally, we comment on several issues raised in recent literature, such as the relationship between completeness and modular invariance, dense sets of charges, and absence of generalized symmetries in the bulk of holographic theories.

arXiv commentInvited Review for Mod. Phys. Lett. A. 15 pages

References in corpus (25)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Generalized Global Symmetries
• Symmetries and Strings in Field Theory and Gravity
• Fracton Phases of Matter
• AdS Dynamics from Conformal Field Theory
• Wormholes, Emergent Gauge Fields, and the Weak Gravity Conjecture
• Emergent Spacetime and Holographic CFTs
• Monopoles, Duality, and String Theory
• Non-Invertible Global Symmetries and Completeness of the Spectrum
• Exotic Symmetries, Duality, and Fractons in 2+1-Dimensional Quantum Field Theory
• Exotic $U(1)$ Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory
• Nets of Subfactors
• Topological Operators and Completeness of Spectrum in Discrete Gauge Theories
• A new handle on three-point coefficients: OPE asymptotics from genus two modular invariance
• Entanglement entropy and superselection sectors I. Global symmetries
• Exotic ${\mathbb{Z}}_N$ Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory
• Generalized free fields and the AdS-CFT correspondence
• Entropic order parameters for the phases of QFT
• The logic of causally closed spacetime subsets
• Quantum Complementarity through Entropic Certainty Principles
• A universal formula for the density of states in theories with finite-group symmetry
• Minimal index and dimension for 2-$C^{\ast }$-categories with finite-dimensional centers
• Variational approach to relative entropies (with application to QFT)
• Gravitational Solitons and Completeness
• Entropic order parameters in weakly coupled gauge theories

Cited by in corpus (18)

• The Weak Gravity Conjecture: A Review
• Generalized Symmetry Breaking Scales and Weak Gravity Conjectures
• Generalized Symmetries of the Graviton
• Developed Method. Interactions and their quantum picture
• Mutual Information of Generalized Free Fields
• Entropic order parameters in weakly coupled gauge theories
• Instability of Universal Terms in the Entanglement Entropy
• Snowmass White Paper: The Quest to Define QFT
• Charges in the UV completion of neutral electrodynamics
• Non-Abelian entanglement asymmetry in random states
• Additivity, Haag duality, and non-invertible symmetries
• Monopole Breaking of Chern-Weil Symmetries
• Baby Universes born from the Void
• ABJ anomaly as a U(1) symmetry and Noether's theorem
• The Luttinger Count is the Homotopy not the Physical Charge: Generalized Anomalies Characterize Non-Fermi Liquids
• Mott Criticality as the Confinement Transition of a Pseudogap-Mott Metal
• Generalized symmetries and Noether's theorem in QFT
• Uniqueness of purifications is equivalent to Haag duality