Global inconsistency, 't Hooft anomaly, and level crossing in quantum mechanics

Abstract

An 't Hooft anomaly is the obstruction for gauging symmetries, and it constrains possible low-energy behaviors of quantum field theories by excluding trivial infrared theories. Global inconsistency condition is recently proposed as a milder condition but is expected to play an almost same role by comparing high symmetry points in the theory space. In order to clarify the consequence coming from this new condition, we discuss several quantum mechanical models with topological angles and explicitly compute their energy spectra. It turns out that the global inconsistency can be saturated not only by the ground-state degeneracy at either of high symmetry points but also by the level crossing (phase transition) separating those high symmetry points.

arXiv comment26 pages, 7 figures

References in corpus (20)

• Fermion Path Integrals And Topological Phases
• Theta Dependence In The Large N Limit Of Four-Dimensional Gauge Theories
• Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence
• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• The "Parity" Anomaly On An Unorientable Manifold
• Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)
• Anomalies of discrete symmetries in three dimensions and group cohomology
• A semiclassical realization of infrared renormalons
• QCD-like Theories on R_3\times S_1: a Smooth Journey from Small to Large r(S_1) with Double-Trace Deformations
• Continuity and Resurgence: towards a continuum definition of the CP(N-1) model
• Resurgence in QFT: Unitons, Fractons and Renormalons in the Principal Chiral Model
• New Methods in QFT and QCD: From Large-N Orbifold Equivalence to Bions and Resurgence
• Quark Masses and Chiral Symmetry
• QCD at θ\sim π
• Non-perturbative Contributions from Complexified Solutions in $\mathbb{C}{P}^{N-1}$ Models
• Chiral Lagrangian from Duality and Monopole Operators in Compactified QCD
• Anomalous Effective Lagrangian and Theta Dependence in QCD at Finite N_c
• Multiflavor QCD* on R_3 x S_1: Studying Transition From Abelian to Non-Abelian Confinement
• Anomalies and chiral symmetry in QCD
• QCD $\theta$-vacua from the chiral limit to the quenched limit

Cited by in corpus (50)

• Anomalies in the Space of Coupling Constants and Their Dynamical Applications II
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications I
• Anomaly and global inconsistency matching: $\theta$-angles, $SU(3)/U(1{)}^2$ nonlinear sigma model, $SU(3)$ chains and its generalizations
• Modified instanton sum in QCD and higher-groups
• Anomaly matching for phase diagram of massless ${\mathbb{Z}}_N$-QCD
• Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly
• Anomaly constraint on massless QCD and the role of Skyrmions in chiral symmetry breaking
• Anomaly matching, (axial) Schwinger models, and high-T super Yang-Mills domain walls
• Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD
• Domain walls in high-T SU(N) super Yang-Mills theory and QCD(adj)
• Fractional $\theta$ angle, 't Hooft anomaly, and quantum instantons in charge-$q$ multi-flavor Schwinger model
• Center vortex and confinement in Yang-Mills theory and QCD with anomaly-preserving compactifications
• Quantum Distillation of Hilbert Spaces, Semi-classics and Anomaly Matching
• Anomaly matching in QCD thermal phase transition
• Lifetimes of (near) eternal false vacua
• Exact-WKB, complete resurgent structure, and mixed anomaly in quantum mechanics on $S^1$
• Topological order in a color-flavor locked phase of $(3+1)$-dimensional $U(N)$ gauge-Higgs system
• Parity and the modular bootstrap
• Lattice Quantum Villain Hamiltonians: Compact scalars, $U(1)$ gauge theories, fracton models and Quantum Ising model dualities
• New Anomalies, TQFTs, and Confinement in Bosonic Chiral Gauge Theories
• Phase structure of the twisted $SU(3)/U(1{)}^2$ flag sigma model on $\mathbb{R}\times S^1$
• On adiabatic cycles of quantum spin systems
• Deconfinement and CP-breaking at $\theta =\pi$ in Yang-Mills theories and a novel phase for SU(2)
• Higher Berry Phase of Fermions and Index Theorem
• Lattice gauge theory for Haldane conjecture and central-branch Wilson fermion
• Universality between vector-like and chiral quiver gauge theories: Anomalies and domain walls
• High-temperature domain walls of QCD with imaginary chemical potentials
• Dihedral symmetry in $SU(N)$ Yang-Mills theory
• Semiclassical analysis of the bifundamental QCD on ${\mathbb{R}}^2\times T^2$ with 't Hooft flux
• Topology of $SU(N)$ lattice gauge theories coupled with ${\mathbb{Z}}_N$ $2$-form gauge fields
• Magnetic operators in 2D compact scalar field theories on the lattice
• Strongly coupled QFT dynamics via TQFT coupling
• Finite-Density Massless Two-Color QCD at Isospin Roberge-Weiss Point and 't Hooft Anomaly
• Lattice regularizations of $\theta$ vacua: Anomalies and qubit models
• Cluster expansion and resurgence in Polyakov model
• Simulating Quantum Mechanics with a $\theta$-term and an 't Hooft Anomaly on a Synthetic Dimension
• Winding theta and destructive interference of instantons
• Role of anomalous symmetry in 0-$\pi$ qubits
• Axial Anomaly in the $SU(N)$ Gauge Matrix Model
• Remarks on effects of projective phase on eigenstate thermalization hypothesis
• Graded Hilbert spaces, quantum distillation and connecting SQCD to QCD
• Center-vortex semiclassics with non-minimal 't Hooft fluxes on ${\mathbb{R}}^2\times T^2$ and center stabilization at large $N$
• Holographic quantum singularity
• Negative string tension of higher-charge Schwinger model via digital quantum simulation
• Charge pumps, pivot Hamiltonians and symmetry-protected topological phases
• Quantum collapse as undecidable proposition in an Everettian multiverse
• Equivariant Parameter Families of Spin Chains: A Discrete MPS Formulation
• The mixed $0$-form/$1$-form anomaly in Hilbert space: pouring new wine into old bottles
• Polyakov Model in 't Hooft flux background: A quantum mechanical reduction with memory
• Large $\theta$ angle in two-dimensional large $N$ ${\mathbb{CP}}^{N-1}$ model