Modified instanton sum in QCD and higher-groups

Abstract

We consider the $SU(N)$ Yang-Mills theory, whose topological sectors are restricted to the instanton number with integer multiples of $p$. We can formulate such a quantum field theory maintaining locality and unitarity, and the model contains both $2\pi$-periodic scalar and $3$-form gauge fields. This can be interpreted as coupling a topological theory to Yang-Mills theory, so the local dynamics becomes identical with that of pure Yang-Mills theory. The theory has not only ${\mathbb{Z}}_N$ $1$-form symmetry but also ${\mathbb{Z}}_p$ $3$-form symmetry, and we study the global nature of this theory from the recent 't Hooft anomaly matching. The computation of 't Hooft anomaly incorporates an intriguing higher-group structure. We also carefully examine that how such kinematical constraint is realized in the dynamics by using the large-$N$ and also the reliable semiclassics on ${\mathbb{R}}^3\times S^1$, and we find that the topological susceptibility plays a role of the order parameter for the ${\mathbb{Z}}_p$ $3$-form symmetry. Introducing a fermion in the fundamental or adjoint representation, we find that the chiral symmetry becomes larger than the usual case by ${\mathbb{Z}}_p$, and it leads to the extra $p$ vacua by discrete chiral symmetry breaking. No dynamical domain wall can interpolate those extra vacua since such objects must be charged under the $3$-form symmetry in order to match the 't Hooft anomaly.

arXiv comment31 pages, 1 figure; (v2) new explanation added, typos fixed, references added

References in corpus (87)

• Generalized Global Symmetries
• Coupling a QFT to a TQFT and Duality
• Reading between the lines of four-dimensional gauge theories
• Theta, Time Reversal, and Temperature
• Periodic Instantons with non-trivial Holonomy
• Exploring 2-Group Global Symmetries
• SU(2) Calorons and Magnetic Monopoles
• Theta Dependence In The Large N Limit Of Four-Dimensional Gauge Theories
• On gauging finite subgroups
• Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence
• Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model
• Monopole Constituents inside SU(n) Calorons
• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• On 2-Group Global Symmetries and Their Anomalies
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications II
• Classifying gauge anomalies through SPT orders and classifying gravitational anomalies through topological orders
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications I
• The "Parity" Anomaly On An Unorientable Manifold
• The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
• Monopoles and Instantons on Partially Compactified D-Branes
• 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
• Notes on generalized global symmetries in QFT
• Exact T-duality between Calorons and Taub-NUT spaces
• Comments on Abelian Higgs Models and Persistent Order
• Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)
• Anomalies of discrete symmetries in three dimensions and group cohomology
• Finite volume QCD at fixed topological charge
• Continuity, Deconfinement, and (Super) Yang-Mills Theory
• GLSM's for gerbes (and other toric stacks)
• A semiclassical realization of infrared renormalons
• 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
• QCD at Fixed Topology
• Walls, Anomalies, and (De)Confinement in Quantum Anti-Ferromagnets
• Universal mechanism of (semi-classical) deconfinement and theta-dependence for all simple groups
• Monopoles, affine algebras and the gluino condensate
• 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
• Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions
• String compactifications on Calabi-Yau stacks
• Modifying the Sum Over Topological Sectors and Constraints on Supergravity
• Anomaly matching for phase diagram of massless ${\mathbb{Z}}_N$-QCD
• Large $N$ reduction with the Twisted Eguchi-Kawai model
• Seiberg-Witten and "Polyakov-like" magnetic bion confinements are continuously connected
• Vacuum structure of bifundamental gauge theories at finite topological angles
• Circle compactification and 't Hooft anomaly
• Abelian gauge theories on the lattice: $\theta$-terms and compact gauge theory with(out) monopoles
• Anomaly constraint on massless QCD and the role of Skyrmions in chiral symmetry breaking
• Neutral bions in the $\mathbb{C}{P}^{N-1}$ model
• Notes on gauging noneffective group actions
• Global symmetries, volume independence and continuity
• Confinement in the bulk, deconfinement on the wall: infrared equivalence between compactified QCD and quantum magnets
• Time Reversal, SU(N) Yang-Mills and Cobordisms: Interacting Topological Superconductors/Insulators and Quantum Spin Liquids in 3+1D
• On time-reversal anomaly of 2+1d topological phases
• From 4d Yang-Mills to 2d ${\mathbb{CP}}^{N-1}$ model: IR problem and confinement at weak coupling
• Sums over topological sectors and quantization of Fayet-Iliopoulos parameters
• Anomaly matching, (axial) Schwinger models, and high-T super Yang-Mills domain walls
• Global inconsistency, 't Hooft anomaly, and level crossing in quantum mechanics
• Lieb-Schultz-Mattis type theorem with higher-form symmetry and the quantum dimer models
• Conflicting Symmetries in Topologically Ordered Surface States of Three-dimensional Bosonic Symmetry Protected Topological Phases
• $\theta$ dependence of 4D $SU(N)$ gauge theories in the large-$N$ limit
• Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD
• Anomaly matching and symmetry-protected critical phases in $SU(N)$ spin systems in 1+1 dimensions
• 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
• Strings from domain walls in supersymmetric Yang-Mills theory and adjoint 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)
• More on time-reversal anomaly of 2+1d topological phases
• 2d affine XY-spin model/ 4d gauge theory duality and deconfinement
• Fractional $\theta$ angle, 't Hooft anomaly, and quantum instantons in charge-$q$ multi-flavor Schwinger model
• The Bi-Fundamental Gauge Theory in 3+1 Dimensions: The Vacuum Structure and a Cascade
• Undoing decomposition
• Dual simulation of the 2d U(1) gauge Higgs model at topological angle $\theta =\pi$: Critical endpoint behavior
• Quantum Distillation of Hilbert Spaces, Semi-classics and Anomaly Matching
• Anomaly matching in QCD thermal phase transition
• Decomposition in diverse dimensions
• Relating 't Hooft Anomalies of 4d Pure Yang-Mills and 2d ${\mathbb{CP}}^{N-1}$ Model
• 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
• $\theta$ dependence in trace deformed $SU(3)$ Yang-Mills theory: a lattice study
• 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
• Domain walls and deconfinement: a semiclassical picture of discrete anomaly inflow
• On the Global Structure of Deformed Yang-Mills Theory and QCD(adj) on ${\mathbb{R}}^3\times {\mathbb{S}}^1$
• The Compactified Principal Chiral Model's Mass Gap

Cited by in corpus (64)

• Symmetries and Strings of Adjoint QCD${}_2$
• Non-invertible 1-form symmetry and Casimir scaling in 2d Yang-Mills theory
• Higher central charges and topological boundaries in 2+1-dimensional TQFTs
• 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
• Discrete Theta Angles, Symmetries and Anomalies
• Global 3-group symmetry and 't Hooft anomalies in axion electrodynamics
• Generalized Symmetry Breaking Scales and Weak Gravity Conjectures
• 8d Supergravity, Reconstruction of Internal Geometry and the Swampland
• Finiteness and the Swampland
• Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD
• Center vortex and confinement in Yang-Mills theory and QCD with anomaly-preserving compactifications
• 1-Form Symmetry, Isolated N=2 SCFTs, and Calabi-Yau Threefolds
• Higher-group symmetry in finite gauge theory and stabilizer codes
• The Weak Gravity Conjecture and Axion Strings
• Lifetimes of (near) eternal false vacua
• Classification of chiral fermionic CFTs of central charge $\le 16$
• Anomaly resolution via decomposition
• Notes on Confinement on ${\mathbf{R}}^3\times {\mathbf{S}}^1$: From Yang-Mills, super-Yang-Mills, and QCD(adj) to QCD(F)
• Quantum symmetries in orbifolds and decomposition
• Deconfinement on axion domain walls
• Semiclassics with 't Hooft flux background for QCD with $2$-index quarks
• Deconfinement and CP-breaking at $\theta =\pi$ in Yang-Mills theories and a novel phase for SU(2)
• Decomposition, Trivially-Acting Symmetries, and Topological Operators
• Modified Villain formulation of abelian Chern-Simons theory
• Topological violation of global symmetries in quantum gravity
• Orbifolds by 2-groups and decomposition
• Elliptic genera of pure gauge theories in two dimensions with semisimple non-simply-connected gauge groups
• A generalization of decomposition in orbifolds
• DMRG study of the higher-charge Schwinger model and its 't Hooft anomaly
• 1-form symmetry versus large N QCD
• Universality between vector-like and chiral quiver gauge theories: Anomalies and domain walls
• Topological modularity of Supermoonshine
• Condensates and anomaly cascade in vector-like theories
• Anomalies, Extensions and Orbifolds
• Semiclassical analysis of the bifundamental QCD on ${\mathbb{R}}^2\times T^2$ with 't Hooft flux
• Notes on two-dimensional pure supersymmetric gauge theories
• Magnetic operators in 2D compact scalar field theories on the lattice
• Higher-group structure in lattice Abelian gauge theory under instanton-sum modification
• Finite-Density Massless Two-Color QCD at Isospin Roberge-Weiss Point and 't Hooft Anomaly
• Strongly coupled QFT dynamics via TQFT coupling
• Study of gapped phases of 4d gauge theories using temporal gauging of the ${\mathbb{Z}}_N$ 1-form symmetry
• Delineating chiral separation effect in two-color dense QCD
• Higher Berry Curvature from the Wave function II: Locally Parameterized States Beyond One Dimension
• Decomposition in Chern-Simons theories in three dimensions
• Decomposition and the Gross-Taylor string theory
• Spectrum of Trace Deformed Yang-Mills Theories
• 3-form Yang-Mills based on 2-crossed modules
• BCF anomaly and higher-group structure in the low energy effective theories of mesons
• Monopole Breaking of Chern-Weil Symmetries
• Higher-Matter and Landau-Ginzburg Theory of Higher-Group Symmetries
• Topological terms and anomaly matching in effective field theories on ${\mathbb{R}}^3\times S^1$: I. Abelian symmetries and intermediate scales
• McKay quivers and decomposition
• Dilaton shifts, probability measures, and decomposition
• (-1)-Form Symmetries and Anomaly Shifting from SymTFT
• Note on lattice description of generalized symmetries in $SU(N)/{\mathbb{Z}}_N$ gauge theories
• Decomposition squared
• Negative string tension of higher-charge Schwinger model via digital quantum simulation
• Vacuum Structures Revisited
• Modeling Dark Matter Halos with Nonlinear Field Theories
• Universal Deformations
• Decomposition in 2d non-invertible gaugings
• Topological Manipulations On $\mathbb{R}$ Symmetries Of Abelian Gauge Theory