Low-Dimensional Long-Range Topological Charge Structure in the QCD Vacuum

Abstract

While sign-coherent 4-dimensional structures cannot dominate topological charge fluctuations in the QCD vacuum at all scales due to reflection positivity, it is possible that enhanced coherence exists over extended space-time regions of lower dimension. Using the overlap Dirac operator to calculate topological charge density, we present evidence for such structure in pure-glue SU(3) lattice gauge theory. It is found that a typical equilibrium configuration is dominated by two oppositely-charged sign-coherent connected structures (``sheets'') covering about 80% of space-time. Each sheet is built from elementary 3-d cubes connected through 2-d faces, and approximates a low-dimensional curved manifold (or possibly a fractal structure) embedded in the 4-d space. At the heart of the sheet is a ``skeleton'' formed by about 18% of the most intense space-time points organized into a global long-range structure, involving connected parts spreading over maximal possible distances. We find that the skeleton is locally 1-dimensional and propose that its geometrical properties might be relevant for understanding the possible role of topological charge fluctuations in the physics of chiral symmetry breaking.

4 pages RevTeX, 4 figures; v2: 6 pages, 5 figures, more explanations provided, figure and references added, published version

References in corpus (23)

• More about exactly massless quarks on the lattice
• The index theorem in QCD with a finite cut-off
• Precision computation of a low-energy reference scale in quenched lattice QCD
• Exact chiral symmetry, topological charge and related topics
• Non-perturbative Renormalisation of Domain Wall Fermions: Quark Bilinears
• Weyl fermions on the lattice and the non-abelian gauge anomaly
• Testing the fixed-point QCD action and the construction of chiral currents
• Aspects of Chiral Symmetry and the Lattice
• Ginsparg-Wilson Relation and Ultralocality
• The U_A(1) Problem on the Lattice with Ginsparg-Wilson Fermions
• Low-lying fermion modes, topology and light hadrons in quenched QCD
• Some more remarks on the Witten-Veneziano formula for the ${\eta }^{\prime }$ mass
• On the Local Structure of Topological Charge Fluctuations in QCD
• A comprehensive picture of topological excitations in finite temperature lattice QCD
• Calorons, instantons and constituent monopoles in SU(3) lattice gauge theory
• Evidence Against Instanton Dominance of Topological Charge Fluctuations in QCD
• Testing the self-duality of topological lumps in SU(3) lattice gauge theory
• Local Chirality of Low-Lying Dirac Eigenmodes and the Instanton Liquid Model
• Chiral fermions on the lattice
• Topology and chiral symmetry breaking in SU(N) gauge theories
• Comment on ``Evidence Against Instanton Dominance of Topological Charge Fluctuations in QCD''
• Strong Non-Ultralocality of Ginsparg-Wilson Fermionic Actions
• The local structure of topological charge fluctuations in QCD

Cited by in corpus (76)

• Theta dependence of SU(N) gauge theories in the presence of a topological term
• 50 Years of Quantum Chromodynamics
• Numerical evidence of chiral magnetic effect in lattice gauge theory
• Exploring the structure of the quenched QCD vacuum with overlap fermions
• A Lattice Study of Quark and Glue Momenta and Angular Momenta in the Nucleon
• Contact Term, its Holographic Description in QCD and Dark Energy
• Center vortices and Dirac eigenmodes in SU(2) lattice gauge theory
• Center Vortices and the Dirac Spectrum
• The Negativity of the Overlap-Based Topological Charge Density Correlator in Pure-Glue QCD and the Non-Integrable Nature of its Contact Part
• Vacuum structure revealed by over-improved stout-link smearing compared with the overlap analysis for quenched QCD
• QCD as a topologically ordered system
• The Parton Orbital Angular Momentum: Status and Prospects
• Inherently Global Nature of Topological Charge Fluctuations in QCD
• Chiral phase transition and Anderson localization in the Instanton Liquid Model for QCD
• Topological susceptibility from the overlap
• Calorons and dyons at the thermal phase transition analyzed by overlap fermions
• The dyonic picture of topological objects in the deconfined phase
• Laplacian modes probing gauge fields
• Generation of confinement and other nonperturbative effects by infrared gluonic degrees of freedom
• Coherent Topological Charge Structure in $C{P}^{N-1}$ Models and QCD
• Three dimensional vacuum domains in four dimensional SU(2) gluodynamics
• Topology across the finite temperature transition studied by overimproved cooling in gluodynamics and QCD
• Chiral superfluidity of the quark-gluon plasma
• Local P Violation Effects and Thermalization in QCD: Views from Quantum Field Theory and Holography
• Topology of dynamical lattice configurations including results from dynamical overlap fermions
• The Reality of the Fundamental Topological Structure in the QCD Vacuum
• Impact of Dynamical Fermions on QCD Vacuum Structure
• Gauge Field Strength Tensor from the Overlap Dirac Operator
• The static quark potential from the gauge invariant Abelian decomposition
• Correlation and localization properties of topological charge density and the pseudoscalar glueball mass in SU(3) lattice Yang-Mills theory
• Calorons in SU(3) lattice gauge theory
• Evidence for fine tuning of fermionic modes in lattice gluodynamics
• P odd fluctuations and Long Range Order in Heavy Ion Collisions. Deformed QCD as a Toy Model
• The Vortex Structure of SU(2) Calorons
• Finite-temperature chiral condensate and low-lying Dirac eigenvalues in quenched SU(2) lattice gauge theory
• Fractal dimension of the topological charge density distribution in SU(2) lattice gluodynamics
• The Analysis of Space-Time Structure in QCD Vacuum I: Localization vs Global Behavior in Local Observables and Dirac Eigenmodes
• SU(2) Gluodynamics and HP1 sigma-model embedding: Scaling, Topology and Confinement
• Is $N=2$ Large?
• The Static Quark Potential from the Gauge Independent Abelian Decomposition
• Adjoint modes as probes of gauge field structure
• Long range order in gauge theories. Deformed QCD as a toy model
• Anomalies, gauge field topology, and the lattice
• Small Instantons in $C{P}^1$ and $C{P}^2$ Sigma Models
• Classical Limits of Scalar and Tensor Gauge Operators Based on the Overlap Dirac Matrix
• Probing the topological structure of the QCD vacuum with overlap fermions
• Confining string and its widening in HP1 embedding approach
• Fractionally charged Wilson loops as a probe of $\theta$-dependence in $C{P}^{N-1}$ sigma models: Instantons vs. large N
• Collisional energy loss and the Chiral Magnetic Effect
• Are the low-momentum gluon correlations semiclassically determined?
• Dependence of asymmetries for charge distribution with respect to the reaction plane on initial energy in heavy ion collisions
• Chiral quark dynamics and topological charge: The role of the Ramond-Ramond U(1) Gauge Field in Holographic QCD
• Lattice Gauge Fields Topology Uncovered by Quaternionic sigma-model Embedding
• Holographic QCD with Topologically Charged Domain-Wall/Membranes
• Topological insulators and the QCD vacuum: the theta parameter as a Berry phase
• Superfluid helium II as the QCD vacuum
• On the Continuum Limit of Topological Charge Density Distribution
• Tachyonic crystals and the laminar instability of the perturbative vacuum in asymptotically free gauge theories
• Filtered topological structure of the QCD vacuum: Effects of dynamical quarks
• Anomaly Inflow and Membrane Dynamics in the QCD Vacuum
• Fine Tuning in Lattice SU(2) Gluodynamics vs Continuum-Theory Constraints
• Improved Measure of Local Chirality
• Glue Spin $S_G$ in The Longitudinally Polarized Nucleon
• Modifying the molecular dynamics action to increase topological tunnelling rate for dynamical overlap fermions
• How Self-Dual is QCD?
• Exploring the QCD vacuum - (some) recent developments in confinement and topology
• Topological Structure of the QCD Vacuum Revealed by Overlap Fermions
• The dependence of overlap topological charge density on Wilson mass parameter
• Probing topological order of QCD at Electron Ion Collider
• Investigating the topological structure of quenched lattice QCD with overlap fermions by using multi-probing approximation
• Bosonization and the Berry connection in two-dimensional QED
• Tensor supercurrent in QCD
• Locality and Efficient Evaluation of Lattice Composite Fields: Overlap-Based Gauge Operators
• Topological Charge Membranes in 2D and 4D Gauge Theory
• Role of the Wilson mass parameter in the overlap Dirac topological charge density
• Influence of Fractal Embedding in Three-Dimensional Euclidean Space on Wave Propagation in Electro- Chromodynamics