Anomalies in the Space of Coupling Constants and Their Dynamical Applications I

Abstract

It is customary to couple a quantum system to external classical fields. One application is to couple the global symmetries of the system (including the Poincaré symmetry) to background gauge fields (and a metric for the Poincaré symmetry). Failure of gauge invariance of the partition function under gauge transformations of these fields reflects 't Hooft anomalies. It is also common to view the ordinary (scalar) coupling constants as background fields, i.e. to study the theory when they are spacetime dependent. We will show that the notion of 't Hooft anomalies can be extended naturally to include these scalar background fields. Just as ordinary 't Hooft anomalies allow us to deduce dynamical consequences about the phases of the theory and its defects, the same is true for these generalized 't Hooft anomalies. Specifically, since the coupling constants vary, we can learn that certain phase transitions must be present. We will demonstrate these anomalies and their applications in simple pedagogical examples in one dimension (quantum mechanics) and in some two, three, and four-dimensional quantum field theories. An anomaly is an example of an invertible field theory, which can be described as an object in (generalized) differential cohomology. We give an introduction to this perspective. Also, we use Quillen's superconnections to derive the anomaly for a free spinor field with variable mass. In a companion paper we will study four-dimensional gauge theories showing how our view unifies and extends many recently obtained results.

arXiv comment76 pages, 1 figure, 2 tables. v2 minor corrections and additional references. v3 published version

References in corpus (60)

• Generalized Global Symmetries
• Symmetries and Strings in Field Theory and Gravity
• Coupling a QFT to a TQFT and Duality
• Reading between the lines of four-dimensional gauge theories
• Theta, Time Reversal, and Temperature
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Exploring 2-Group Global Symmetries
• Level/rank Duality and Chern-Simons-Matter Theories
• On gauging finite subgroups
• On 2-Group Global Symmetries and Their Anomalies
• Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications II
• D-brane Charges in Five-brane backgrounds
• Time-Reversal Breaking in QCD${}_4$, Walls, and Dualities in 2+1 Dimensions
• Comments on Global Symmetries, Anomalies, and Duality in (2+1)d
• Comments on Abelian Higgs Models and Persistent Order
• Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups
• GLSM's for gerbes (and other toric stacks)
• Supersymmetric Index In Four-Dimensional Gauge Theories
• Anomalies, Conformal Manifolds, and Spheres
• Setting the quantum integrand of M-theory
• Heisenberg Groups and Noncommutative Fluxes
• Walls, Anomalies, and (De)Confinement in Quantum Anti-Ferromagnets
• Anomaly and global inconsistency matching: $\theta$-angles, $SU(3)/U(1{)}^2$ nonlinear sigma model, $SU(3)$ chains and its generalizations
• Anomaly constraints on deconfinement and chiral phase transition
• Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups
• Modifying the Sum Over Topological Sectors and Constraints on Supergravity
• Non-birational twisted derived equivalences in abelian GLSMs
• Anomaly matching for phase diagram of massless ${\mathbb{Z}}_N$-QCD
• Phases Of Adjoint QCD${}_3$ And Dualities
• A Symmetry Breaking Scenario for QCD${}_3$
• Differential cohomology in a cohesive infinity-topos
• Notes on gauging noneffective group actions
• Three-dimensional dualities with bosons and fermions
• Time-Reversal Symmetry, Anomalies, and Dualities in (2+1)$d$
• Generalization of the Haldane conjecture to SU(3) chains
• Anomalies of Duality Groups and Extended Conformal Manifolds
• Global inconsistency, 't Hooft anomaly, and level crossing in quantum mechanics
• Order parameters and color-flavor center symmetry in QCD
• Candidate Phases for SU(2) Adjoint QCD${}_4$ with Two Flavors from $\mathcal{N}=2$ Supersymmetric Yang-Mills Theory
• Domain walls in high-T SU(N) super Yang-Mills theory and QCD(adj)
• A note on the $(\infty ,n)$-category of cobordisms
• Anomaly of the Electromagnetic Duality of Maxwell Theory
• The Bi-Fundamental Gauge Theory in 3+1 Dimensions: The Vacuum Structure and a Cascade
• Topological order in a color-flavor locked phase of $(3+1)$-dimensional $U(N)$ gauge-Higgs system
• Sigma Models on Flags
• Exceptional Chern-Simons-Matter Dualities
• Living on the walls of super-QCD
• Anomalies involving the space of couplings and the Zamolodchikov metric
• Shortening Anomalies in Supersymmetric Theories
• Phase structure of the twisted $SU(3)/U(1{)}^2$ flag sigma model on $\mathbb{R}\times S^1$
• On the Cohomology of the Classifying Spaces of Projective Unitary Groups
• Theories of Class F and Anomalies
• Moduli Anomalies and Local Terms in the Operator Product Expansion
• Osborn Equation and Irrelevant Operators
• Superconnections and Index Theory
• The cobordism hypothesis
• Topological Terms and Phases of Sigma Models
• Conformal field theories and compact curves in moduli spaces
• The Free Fermion Anomaly and Representations of the Pin Groups

Cited by in corpus (128)

• Generalized Symmetries in Condensed Matter
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications II
• Non-Invertible Global Symmetries and Completeness of the Spectrum
• Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases
• Generalized Global Symmetries of $T[M]$ Theories. I
• Lieb-Schultz-Mattis, Luttinger, and 't Hooft -- anomaly matching in lattice systems
• Topological Transition on the Conformal Manifold
• Majorana chain and Ising model -- (non-invertible) translations, anomalies, and emanant symmetries
• Foliated Quantum Field Theory of Fracton Order
• A Modified Villain Formulation of Fractons and Other Exotic Theories
• Modified instanton sum in QCD and higher-groups
• Topological Holography: Towards a Unification of Landau and Beyond-Landau Physics
• Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly
• Chern-Weil Global Symmetries and How Quantum Gravity Avoids Them
• Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond $N$-ality
• Higher-form symmetries and 3-group in axion electrodynamics
• Higher-Form Symmetries and Their Anomalies in M-/F-Theory Duality
• Symmetry-Enriched Quantum Spin Liquids in $(3+1)d$
• Global 3-group symmetry and 't Hooft anomalies in axion electrodynamics
• Generalized Symmetry Breaking Scales and Weak Gravity Conjectures
• Discrete and higher-form symmetries in SCFTs from wrapped M5-branes
• String Universality and Non-Simply-Connected Gauge Groups in 8d
• Berry Phase in Quantum Field Theory: Diabolical Points and Boundary Phenomena
• Continuous Generalized Symmetries in Three Dimensions
• Anomaly Inflow for Subsystem Symmetries
• On anomalies and gauging of U(1) non-invertible symmetries in 4d QED
• Anomaly Obstructions to Symmetry Preserving Gapped Phases
• Baby Universes, Holography, and the Swampland
• Finiteness and the Swampland
• Higher Form Symmetries TFT in 6d
• Higher-dimensional generalizations of the Berry curvature
• Instantons, Symmetries and Anomalies in Five Dimensions
• M5-brane Sources, Holography, and Argyres-Douglas Theories
• Enhanced thermal Hall effect in the square-lattice Néel state
• The anomaly that was not meant IIB
• Global 4-group symmetry and 't Hooft anomalies in topological axion electrodynamics
• Anomalies and gauging of U(1) symmetries
• Matrix ensembles with global symmetries and 't Hooft anomalies from 2d gauge theory
• On the baryon-color-flavor (BCF) anomaly in vector-like theories
• Fractons with Twisted Boundary Conditions and Their Symmetries
• Center vortex and confinement in Yang-Mills theory and QCD with anomaly-preserving compactifications
• Symmetries and Anomalies of (1+1)d Theories: 2-groups and Symmetry Fractionalization
• Evidence for a Non-Supersymmetric 5d CFT from Deformations of 5d $SU(2)$ SYM
• Revisiting Wess-Zumino-Witten terms
• The Weak Gravity Conjecture and Axion Strings
• Lifetimes of (near) eternal false vacua
• Quantum many-body topology of quasicrystals
• Topological order in a color-flavor locked phase of $(3+1)$-dimensional $U(N)$ gauge-Higgs system
• Line Operators of Gauge Theories on Non-Spin Manifolds
• Flow of (higher) Berry curvature and bulk-boundary correspondence in parametrized quantum systems
• Generalized 't Hooft anomalies on non-spin manifolds
• Field theories with higher-group symmetry from composite currents
• Topological Goldstone phases of matter
• From 3d dualities to hadron physics
• Cobordism and Deformation Class of the Standard Model
• Topological aspects of $4$D Abelian lattice gauge theories with the $\theta$ parameter
• Deconfinement on axion domain walls
• On adiabatic cycles of quantum spin systems
• Topological modular forms and the absence of all heterotic global anomalies
• M5-branes Probing Flux Backgrounds
• Deconfinement and CP-breaking at $\theta =\pi$ in Yang-Mills theories and a novel phase for SU(2)
• Vector dominance, one flavored baryons, and QCD domain walls from the "hidden" Wess-Zumino term
• Gauge Enhanced Quantum Criticality and Time Reversal Domain Wall: SU(2) Yang-Mills Dynamics with Topological Terms
• Higher Berry Phase of Fermions and Index Theorem
• Topological defects
• Anomaly inflow and $p$-form gauge theories
• Universality between vector-like and chiral quiver gauge theories: Anomalies and domain walls
• Condensates and anomaly cascade in vector-like theories
• Vector mesons on the wall
• Four-fermion deformations of the massless Schwinger model and confinement
• Topology of $SU(N)$ lattice gauge theories coupled with ${\mathbb{Z}}_N$ $2$-form gauge fields
• An integrable spin chain with Hilbert space fragmentation and solvable real time dynamics
• Definition and Classification of Fermi Surface Anomalies
• Multi wavefunction overlap and multi entropy for topological ground states in (2+1) dimensions
• Higgs-Confinement Transitions in QCD from Symmetry Protected Topological Phases
• Conformal Contact Terms and Semi-Local Terms
• The Fate of Discrete 1-Form Symmetries in 6d
• Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED
• Witten effect, anomaly inflow, and charge teleportation
• Magnetic operators in 2D compact scalar field theories on the lattice
• Generalized chiral instabilities, linking numbers, and non-invertible symmetries
• On Topology of the Moduli Space of Gapped Hamiltonians for Topological Phases
• Higher-group structure in lattice Abelian gauge theory under instanton-sum modification
• Symmetry Transmutation and Anomaly Matching
• Global anomaly matching in higher-dimensional ${\mathbb{CP}}^{N-1}$ model
• Finite-Density Massless Two-Color QCD at Isospin Roberge-Weiss Point and 't Hooft Anomaly
• Higher Berry Curvature from the Wave Function I: Schmidt Decomposition and Matrix Product States
• Charting the space of ground states with tensor networks
• Anomaly Matching Across Dimensions and Supersymmetric Cardy Formulae
• Remarks on Berry Connection in QFT, Anomalies, and Applications
• Higher Berry Curvature from the Wave function II: Locally Parameterized States Beyond One Dimension
• Ferromagnets, a New Anomaly, Instantons, and (noninvertible) Continuous Translations
• Geometric Approach to 3D Interfaces at Strong Coupling
• Spontaneous symmetry breaking in pure 2D Yang-Mills theory
• Anomaly and Superconnection
• Differential models for the Anderson dual to bordism theories and invertible QFT's, II
• Gappability Index for Quantum Many-Body Systems
• Lattice regularizations of $\theta$ vacua: Anomalies and qubit models
• A Long Exact Sequence in Symmetry Breaking: order parameter constraints, defect anomaly-matching, and higher Berry phases
• Anomalous Continuous Translations
• LSM and CPT
• Winding theta and destructive interference of instantons
• Monopole Breaking of Chern-Weil Symmetries
• Charge pumps, boundary modes, and the necessity of unnecessary criticality
• Global Aspects of Spaces of Vacua
• Instanton Density Operator in Lattice QCD from Higher Category Theory
• Disturbing news about the $d=2+\epsilon$ expansion
• Non-Invertible Gauss Law and Axions
• Center-vortex semiclassics with non-minimal 't Hooft fluxes on ${\mathbb{R}}^2\times T^2$ and center stabilization at large $N$
• (-1)-Form Symmetries and Anomaly Shifting from SymTFT
• Higher-group global symmetry and the bosonic M5 brane
• Infinite Distance Limits and Information Theory
• Real-Time Corrections to the Effective Potential
• Negative string tension of higher-charge Schwinger model via digital quantum simulation
• Strong CP from a Hidden Chiral Condensate
• Modulating Hamiltonian Approach to Quantum Many-Body Systems and Crystalline Topological Phases Protected by Generalized Magnetic Translations
• Smooth generalized symmetries of quantum field theories
• Interface Junctions in QCD${}_4$
• Charge pumps, pivot Hamiltonians and symmetry-protected topological phases
• Universal Deformations
• Equivariant Parameter Families of Spin Chains: A Discrete MPS Formulation
• Intertwined order of generalized global symmetries
• Anomaly-induced edge currents in hydrodynamics with parity anomaly
• Topological Manipulations On $\mathbb{R}$ Symmetries Of Abelian Gauge Theory
• Large $\theta$ angle in two-dimensional large $N$ ${\mathbb{CP}}^{N-1}$ model
• Symmetry TFTs from String Theory
• Baryons, Skyrmions and $\theta$-periodicity anomaly in chiral and vector-like gauge theories
• Revisiting the $k$-theorem with the ANEC