Fractional $\theta$ angle, 't Hooft anomaly, and quantum instantons in charge-$q$ multi-flavor Schwinger model

Abstract

This work examines non-perturbative dynamics of a $2$-dimensional QFT by using discrete 't Hooft anomaly, semi-classics with circle compactification and bosonization. We focus on charge-$q$ $N$-flavor Schwinger model, and also Wess-Zumino-Witten model. We first apply the recent developments of discrete 't Hooft anomaly matching to theories on ${\mathbb{R}}^2$ and its compactification to $\mathbb{R}\times S_L^1$. We then compare the 't Hooft anomaly with dynamics of the models by explicitly constructing eigenstates and calculating physical quantities on the cylinder spacetime with periodic and flavor-twisted boundary conditions. We find different boundary conditions realize different anomalies. Especially under the twisted boundary conditions, there are $Nq$ vacua associated with discrete chiral symmetry breaking. Chiral condensates for this case have fractional $\theta$ dependence ${\mathrm{e}}^{\mathrm{i}\theta /Nq}$, which provides the $Nq$-branch structure with soft fermion mass. We show that these behaviors at a small circumference cannot be explained by usual instantons but should be understood by "quantum" instantons, which saturate the BPS bound between classical action and quantum-induced effective potential. The effects of the quantum-instantons match the exact results obtained via bosonization within the region of applicability of semi-classics. We also argue that large-$N$ limit of the Schwinger model with twisted boundary conditions satisfy volume independence.

arXiv comment69 pages, 9 figures, (v2) minor updates of intro, (v3) typos fixed

References in corpus (63)

• Generalized Global Symmetries
• Coupling a QFT to a TQFT and Duality
• Theta, Time Reversal, and Temperature
• Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model
• The "Parity" Anomaly On An Unorientable Manifold
• Volume independence in large Nc QCD-like gauge theories
• The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
• Time-Reversal Breaking in QCD${}_4$, Walls, and Dualities in 2+1 Dimensions
• Field theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology and beyond
• Comments on Abelian Higgs Models and Persistent Order
• Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)
• Continuity, Deconfinement, and (Super) Yang-Mills Theory
• 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
• Walls, Anomalies, and (De)Confinement in Quantum Anti-Ferromagnets
• New Methods in QFT and QCD: From Large-N Orbifold Equivalence to Bions and Resurgence
• Anomaly and global inconsistency matching: $\theta$-angles, $SU(3)/U(1{)}^2$ nonlinear sigma model, $SU(3)$ chains and its generalizations
• Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions
• The Massive Multi-flavor Schwinger Model
• Finite size phase transitions in QCD with adjoint fermions
• Anomaly matching for phase diagram of massless ${\mathbb{Z}}_N$-QCD
• Vacuum structure of bifundamental gauge theories at finite topological angles
• Circle compactification and 't Hooft anomaly
• Anomaly constraint on massless QCD and the role of Skyrmions in chiral symmetry breaking
• Neutral bions in the $\mathbb{C}{P}^{N-1}$ model
• Confinement in the bulk, deconfinement on the wall: infrared equivalence between compactified QCD and quantum magnets
• Global symmetries, volume independence and continuity
• Time Reversal, SU(N) Yang-Mills and Cobordisms: Interacting Topological Superconductors/Insulators and Quantum Spin Liquids in 3+1D
• Adjoint QCD on ${\mathbb{R}}^3\times S^1$ with twisted fermionic boundary conditions
• Non-perturbative Contributions from Complexified Solutions in $\mathbb{C}{P}^{N-1}$ Models
• Generalization of the Haldane conjecture to SU(3) chains
• From 4d Yang-Mills to 2d ${\mathbb{CP}}^{N-1}$ model: IR problem and confinement at weak coupling
• On time-reversal anomaly of 2+1d topological phases
• Anomaly matching, (axial) Schwinger models, and high-T super Yang-Mills domain walls
• Global inconsistency, 't Hooft anomaly, and level crossing in quantum mechanics
• C-P-T anomaly matching in bosonic quantum field theory and spin chains
• Classifying bions in Grassmann sigma models and non-Abelian gauge theories by D-branes
• Chiral Lagrangian from Duality and Monopole Operators in Compactified QCD
• Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb{C}{P}^{N-1}$ models
• Domain walls in high-T SU(N) super Yang-Mills theory and QCD(adj)
• Large N Volume Independence and an Emergent Fermionic Symmetry
• Chiral Symmetry Breaking without Bilinear Condensates, Unbroken Axial Z_N Symmetry, and Exact QCD Inequalities
• Haldane limits via Lagrangian embeddings
• Deconfinement in N=1 super Yang-Mills theory on R^3 x S^1 via dual-Coulomb gas and "affine" XY-model
• Confinement and Z_3 symmetry in three-flavor QCD
• Quantum Distillation of Hilbert Spaces, Semi-classics and Anomaly Matching
• The curious incident of multi-instantons and the necessity of Lefschetz thimbles
• Anomaly matching in QCD thermal phase transition
• Lattice study on QCD-like theory with exact center symmetry
• Differences and similarities between fundamental and adjoint matters in SU(N) gauge theories
• Relating 't Hooft Anomalies of 4d Pure Yang-Mills and 2d ${\mathbb{CP}}^{N-1}$ Model
• Sigma Models on Flags
• Multi-flavor massless QED${}_2$ at finite densities via Lefschetz thimbles
• QED With Unequal Charges: A study of spontaneous Zn symmetry breaking
• Non-BPS exact solutions and their relation to bions in $\mathbb{C}{P}^{N-1}$ models
• Resurgence Structure to All Orders of Multi-bions in Deformed SUSY Quantum Mechanics
• Vacuum Structure of Charge k Two-Dimensional QED and Dynamics of an Anti D-String Near an O1- plane
• Understanding of QCD at high density from Z3-symmetric QCD-like theory
• Fractional instanton of the SU($3$) gauge theory in weak coupling regime
• Phase structure of the twisted $SU(3)/U(1{)}^2$ flag sigma model on $\mathbb{R}\times S^1$
• High-temperature domain walls of QCD with imaginary chemical potentials
• Chiral symmetry breaking with no bilinear condensate revisited

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• Higher-group structure in $2n$-dimensional axion-electrodynamics
• Finite-Density Massless Two-Color QCD at Isospin Roberge-Weiss Point and 't Hooft Anomaly
• Strongly coupled QFT dynamics via TQFT coupling
• Topological mass generation in gapless systems
• BCF anomaly and higher-group structure in the low energy effective theories of mesons
• Spontaneous symmetry breaking in pure 2D Yang-Mills theory
• Monopole-vortex continuity of $\mathcal{N}=1$ super Yang-Mills theory on ${\mathbb{R}}^2\times S^1\times S^1$ with 't Hooft twist
• Winding theta and destructive interference of instantons
• ${\mathbb{Z}}_N$ stability and continuity in twisted Eguchi-Kawai model with two-flavor adjoint fermions
• Negative string tension of higher-charge Schwinger model via digital quantum simulation
• Vacuum Structures Revisited
• Universal Deformations
• The mixed $0$-form/$1$-form anomaly in Hilbert space: pouring new wine into old bottles
• Nonperturbative signatures of fractons in the twisted multiflavor Schwinger Model