Chern-Weil Global Symmetries and How Quantum Gravity Avoids Them

Abstract

We draw attention to a class of generalized global symmetries, which we call "Chern-Weil global symmetries," that arise ubiquitously in gauge theories. The Noether currents of these Chern-Weil global symmetries are given by wedge products of gauge field strengths, such as $F_2\wedge H_3$ and $\text{tr}(F_2^2)$, and their conservation follows from Bianchi identities. As a result, they are not easy to break. However, it is widely believed that exact global symmetries are not allowed in a consistent theory of quantum gravity. As a result, any Chern-Weil global symmetry in a low-energy effective field theory must be either broken or gauged when the theory is coupled to gravity. In this paper, we explore the processes by which Chern-Weil symmetries may be broken or gauged in effective field theory and string theory. We will see that many familiar phenomena in string theory, such as axions, Chern-Simons terms, worldvolume degrees of freedom, and branes ending on or dissolving in other branes, can be interpreted as consequences of the absence of Chern-Weil symmetries in quantum gravity, suggesting that they might be general features of quantum gravity. We further discuss implications of breaking and gauging Chern-Weil symmetries for particle phenomenology and for boundary CFTs of AdS bulk theories. Chern-Weil global symmetries thus offer a unified framework for understanding many familiar aspects of quantum field theory and quantum gravity.

arXiv comment62 pages + appendices, 5 figures. v2: References added

References in corpus (118)

• Generalized Global Symmetries
• Axions In String Theory
• The String Landscape, Black Holes and Gravity as the Weakest Force
• Monodromy in the CMB: Gravity Waves and String Inflation
• Symmetries and Strings in Field Theory and Gravity
• Gravity Waves and Linear Inflation from Axion Monodromy
• Massless Black Holes and Conifolds in String Theory
• Small Instantons in String Theory
• Planck-Scale Physics and the Peccei-Quinn Mechanism
• Completing Natural Inflation
• Phase Transitions In M-Theory And F-Theory
• Coupling a QFT to a TQFT and Duality
• Reading between the lines of four-dimensional gauge theories
• Tachyon Dynamics in Open String Theory
• Comments on String Dynamics in Six Dimensions
• I-Brane Inflow and Anomalous Couplings on D-Branes
• Solutions to the strong CP problem in a world with gravity
• A Natural Framework for Chaotic Inflation
• Small $E_8$ Instantons and Tensionless Non-critical Strings
• The QCD Axion and Moduli Stabilisation
• Exploring 2-Group Global Symmetries
• Infinite Distances in Field Space and Massless Towers of States
• On the Classification of 6D SCFTs and Generalized ADE Orbifolds
• AdS and the Swampland
• Atomic Classification of 6D SCFTs
• Gauge Fields and D-branes
• Wormholes, Emergent Gauge Fields, and the Weak Gravity Conjecture
• Branes and Six Dimensional Supersymmetric Theories
• An Ignoble Approach to Large Field Inflation
• Monopoles, Duality, and String Theory
• Baryons and Domain Walls in an N = 1 Superconformal Gauge Theory
• Non-trivial Fixed Points of The Renormalization Group in Six Dimensions
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications II
• Constraints on symmetry from holography
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications I
• Evidence for a Lattice Weak Gravity Conjecture
• Non-Invertible Global Symmetries and Completeness of the Spectrum
• Anomaly Cancellations in the Type I D9-anti-D9 System and the USp(32) String Theory
• All AdS_7 solutions of type II supergravity
• Emergence and the Swampland Conjectures
• Anomaly polynomial of general 6d SCFTs
• Sharpening the Weak Gravity Conjecture with Dimensional Reduction
• Non-abelian Tensor-multiplet Anomalies
• The Weak Gravity Conjecture in three dimensions
• F-term Axion Monodromy Inflation
• AdS/CFT Correspondence And Topological Field Theory
• A Tower Weak Gravity Conjecture from Infrared Consistency
• The dual superconformal theory for Lpqr manifolds
• Holography for (1,0) theories in six dimensions
• The Weak Gravity Conjecture and Emergence from an Ultraviolet Cutoff
• Surprises in Open-String Perturbation Theory
• Anti-de Sitter Space and the Center of the Gauge Group
• AdS_5 x S^5 Untwisted
• S-folds and 4d N=3 superconformal field theories
• Higher-derivative couplings in string theory: dualities and the B-field
• On orbifolds of M-Strings
• Of CP and other Gauge Symmetries in String Theory
• Non-Abelian discrete gauge symmetries in 4d string models
• Top Down Approach to 6D SCFTs
• 2-Group Global Symmetries and Anomalies in Six-Dimensional Quantum Field Theories
• Swampland Conjectures for Strings and Membranes
• String universality in ten dimensions
• Topological Operators and Completeness of Spectrum in Discrete Gauge Theories
• Cobordism Conjecture, Anomalies, and the String Lamppost Principle
• Modified instanton sum in QCD and higher-groups
• Chern-Simons terms and the Three Notions of Charge
• Instanton operators and symmetry enhancement in 5d supersymmetric gauge theories
• A violation of global symmetries from replica wormholes and the fate of black hole remnants
• Global symmetry, Euclidean gravity, and the black hole information problem
• Branes and the Swampland
• 6d holographic anomaly match as a continuum limit
• Invariant tensors for simple groups
• Higher-form symmetries of 6d and 5d theories
• Six-Dimensional Superconformal Theories and their Compactifications from Type IIA Supergravity
• Generalized global symmetries and holography
• Photon Masses in the Landscape and the Swampland
• Higher-form symmetries and 3-group in axion electrodynamics
• Why are fractional charges of orientifolds compatible with Dirac quantization?
• Global 3-group symmetry and 't Hooft anomalies in axion electrodynamics
• Anomalies and inflow on D-branes and O-planes
• Minkowski 3-forms, Flux String Vacua, Axion Stability and Naturalness
• String Universality and Non-Simply-Connected Gauge Groups in 8d
• String Universality for Permutation Orbifolds
• Three-Form Gauging of axion Symmetries and Gravity
• Open string multi-branched and Kahler potentials
• Kaluza-Klein Dyons in String Theory
• Four Dimensional $\mathcal{N}=4$ SYM and the Swampland
• Baby Universes, Holography, and the Swampland
• Signatures of global symmetry violation in relative entropies and replica wormholes
• Cobordism Classes and the Swampland
• Fission, Fusion, and 6D RG Flows
• Instantons, Symmetries and Anomalies in Five Dimensions
• The frozen phase of F-theory
• The Type IIA Flux Potential, 4-forms and Freed-Witten anomalies
• A Note on the Chiral Anomaly in the AdS/CFT Correspondence and 1/N^2 Correction
• 8d gauge anomalies and the topological Green-Schwarz mechanism
• Revisiting the classifications of 6d SCFTs and LSTs
• AdS${}_7$/CFT${}_6$ with orientifolds
• A Chern-Simons Pandemic
• What is the Magnetic Weak Gravity Conjecture for Axions?
• Swampland Constraints on 5d $\mathcal{N}=1$ Supergravity
• Spacetime and Universal Soft Modes --- Black Holes and Beyond
• Instanton Operators in Five-Dimensional Gauge Theories
• How many fluxes fit in an EFT?
• General Prescription for Global U(1)'s in 6D SCFTs
• Higher-form symmetries and spontaneous symmetry breaking
• Born-Infeld Action and Chern-Simons Term from Kaluza-Klein Monopole in M-theory
• Charges and holography in 6d (1,0) theories
• An SL(2,Z) anomaly in IIB supergravity and its F-theory interpretation
• 6d strings and exceptional instantons
• Topological violation of global symmetries in quantum gravity
• Axion Periodicity and Coupling Quantization in the Presence of Mixing
• Theta-problem and the String Swampland
• A Note on 4D Heterotic String Vacua, FI-terms and the Swampland
• Gauge and gravitational instantons: From 3-forms and fermions to Weak Gravity and flat axion potentials
• The Fate of Discrete 1-Form Symmetries in 6d
• Closed Strings from SO(8) Yang-Mills Instantons
• Discrete anomalies in supergravity and consistency of string backgrounds

Cited by in corpus (27)

• Non-Invertible Global Symmetries and Completeness of the Spectrum
• The Weak Gravity Conjecture: A Review
• Generalized Symmetry Breaking Scales and Weak Gravity Conjectures
• Higher Symmetries of 5d Orbifold SCFTs
• Continuous Generalized Symmetries in Three Dimensions
• Finiteness and the Swampland
• Compactness of Brane Moduli and the String Lamppost Principle in $d>6$
• Global 4-group symmetry and 't Hooft anomalies in topological axion electrodynamics
• Higher-group symmetry in finite gauge theory and stabilizer codes
• Cosmic strings from pure Yang-Mills theory
• Asymptotic Observables and the Swampland
• Axion Mass from Magnetic Monopole Loops
• The Weak Gravity Conjecture and Axion Strings
• Tameness, Strings, and the Distance Conjecture
• Pure Supersymmetric AdS and the Swampland
• Non-Invertible Symmetries in Supergravity
• Dimensional Reduction of Cobordism and K-theory
• Looking for structure in the cobordism conjecture
• Constraints on Early Dark Energy from the Axion Weak Gravity Conjecture
• Gravitational Solitons and Completeness
• A fresh view on string orbifolds
• The Inflated Chern-Simons Number in Spectator Chromo-Natural Inflation
• Modular Curves and the Refined Distance Conjecture
• Higher-group structure in $2n$-dimensional axion-electrodynamics
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
• Unstable Nambu-Goldstone modes
• State counting on fibered CY-3 folds and the non-Abelian Weak Gravity Conjecture