Non-Invertible Gauss Law and Axions

Abstract

In axion-Maxwell theory at the minimal axion-photon coupling, we find non-invertible 0- and 1-form global symmetries arising from the naive shift and center symmetries. Since the Gauss law is anomalous, there is no conserved, gauge-invariant, and quantized electric charge. Rather, using half higher gauging, we find a non-invertible Gauss law associated with a non-invertible 1-form global symmetry, which is related to the Page charge. These symmetries act invertibly on the axion field and Wilson line, but non-invertibly on the monopoles and axion strings, leading to selection rules related to the Witten effect. We also derive various crossing relations between the defects. The non-invertible 0- and 1-form global symmetries mix with other invertible symmetries in a way reminiscent of a higher-group symmetry. Using this non-invertible higher symmetry structure, we derive universal inequalities on the energy scales where different infrared symmetries emerge in any renormalization group flow to the axion-Maxwell theory. Finally, we discuss implications for the Weak Gravity Conjecture and the Completeness Hypothesis in quantum gravity.

57 pages; v2: sec 7.3 added; v3: minor edits

References in corpus (50)

• Generalized Global Symmetries
• Symmetries and Strings in Field Theory and Gravity
• Interacting anyons in topological quantum liquids: The golden chain
• Duality and defects in rational conformal field theory
• Generalized Symmetries in Condensed Matter
• Higher Gauging and Non-invertible Condensation Defects
• Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d
• Non-Invertible Higher-Categorical Symmetries
• Universal Non-Invertible Symmetries
• Asymptotic density of states in 2d CFTs with non-invertible symmetries
• Non-Invertible Symmetries from Holography and Branes
• Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases
• The Branes Behind Generalized Symmetry Operators
• Construction of two-dimensional topological field theories with non-invertible symmetries
• Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond
• Non-invertible Time-reversal Symmetry
• Global Dipole Symmetry, Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons
• Topological Defects on the Lattice: Dualities and Degeneracies
• Branes and Non-Invertible Symmetries
• Exploring Non-Invertible Symmetries in Free Theories
• On Continuous 2-Category Symmetries and Yang-Mills Theory
• Non-invertible Symmetries of Class $\mathcal{S}$ Theories
• Braided fusion categories, gravitational anomalies, and the mathematical framework for topological orders in any dimensions
• Topological Holography: Towards a Unification of Landau and Beyond-Landau Physics
• Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond $N$-ality
• Non-invertible Symmetries and Higher Representation Theory I
• Higher-form symmetries and 3-group in axion electrodynamics
• Non-Invertible Defects in 5d, Boundaries and Holography
• Decomposition, condensation defects, and fusion
• Generalized Symmetry Breaking Scales and Weak Gravity Conjectures
• Fusion Category Symmetry II: Categoriosities at c = 1 and Beyond
• Continuous Generalized Symmetries in Three Dimensions
• Anomalies and Symmetry Fractionalization
• On anomalies and gauging of U(1) non-invertible symmetries in 4d QED
• Non-Invertible Symmetries from Discrete Gauging and Completeness of the Spectrum
• Mixed Anomalies, Two-groups, Non-Invertible Symmetries, and 3d Superconformal Indices
• Numerical evidence for a Haagerup conformal field theory
• A critical lattice model for a Haagerup conformal field theory
• Topological Defect Lines in Two Dimensional Fermionic CFTs
• Gauging Noninvertible Defects: A 2-Categorical Perspective
• Axion Mass from Magnetic Monopole Loops
• Fermionization of fusion category symmetries in 1+1 dimensions
• Gauge Enhanced Quantum Criticality Between Grand Unifications: Categorical Higher Symmetry Retraction
• Non-invertible symmetries in axion electrodynamics
• Decomposition, Trivially-Acting Symmetries, and Topological Operators
• Line Defect Quantum Numbers & Anomalies
• Non-invertible topological defects in 4-dimensional ${\mathbb{Z}}_2$ pure lattice gauge theory
• Gravitational Solitons and Completeness
• Higher-group structure in $2n$-dimensional axion-electrodynamics
• $\mathbb{Q}/\mathbb{Z}$ symmetry

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