On the Local Structure of Topological Charge Fluctuations in QCD

Abstract

We consider the lattice topological charge density introduced by Hasenfratz, Laliena and Niedermayer and propose its eigenmode expansion as a tool to investigate the structure of topological charge fluctuations in QCD. The resulting effective density is built from local chiralities studied previously. At every order of the expansion the density exactly sums up to the global topological charge, and the leading term describes the maximally smooth space-time distribution of charge relevant for propagating light fermions. We use this framework to demonstrate our previous suggestion that the bulk of topological charge in QCD does not effectively appear in the form of quantized unit lumps. Our conclusion implies that it is unlikely that the mixing of "would-be" zeromodes associated with such lumps is the prevalent microscopic mechanism for spontaneous chiral symmetry breaking in QCD. We also present first results quantitatively characterizing the space-time behavior of effective densities. For coherent fluctuations contained in spherical regions we find a continuous distribution of associated charges essentially ending at ~0.5.

arXiv comment5 pages, 4 figures, RevTex; v2: typo in eq. (3) fixed; v3: References added, minor cosmetic changes, unchanged conclusions, published version

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• Center vortices and Dirac eigenmodes in SU(2) lattice gauge theory
• 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
• Calorons, instantons and constituent monopoles in SU(3) lattice gauge theory
• 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
• Laplacian modes probing gauge fields
• Quantitative comparison of filtering methods in lattice QCD
• Topology of dynamical lattice configurations including results from dynamical overlap fermions
• The Reality of the Fundamental Topological Structure in the QCD Vacuum
• Topological lumps and Dirac zero modes in SU(3) lattice gauge theory on the torus
• Impact of Dynamical Fermions on QCD Vacuum Structure
• Cautionary remarks on the moduli space metric for multi-dyon simulations
• Evidence for fine tuning of fermionic modes in lattice gluodynamics
• Recombination of dyons into calorons in SU(2) lattice fields at low temperatures
• 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
• Wilson mass dependence of the overlap topological charge density
• Adjoint modes as probes of gauge field structure
• Confinement from semiclassical gluon fields in SU(2) gauge theory
• Probing the topological structure of the QCD vacuum with overlap fermions
• Confining string and its widening in HP1 embedding approach
• Fractional topological charge in $SU(N)$ gauge theories without dynamical quarks
• Matter of resolution: from quasiclassics to fine tuning
• Lattice Gauge Fields Topology Uncovered by Quaternionic sigma-model Embedding
• Ultraviolet filtering of lattice configurations and applications to Monte Carlo dynamics
• Evaluating topological charge density with symmetric multi-probing method
• Metal or Insulator? Dirac operator spectrum in holographic QCD
• Gauge Singularities in the SU(2) Vacuum on the Lattice
• Improved Measure of Local Chirality
• Topological Structure of the QCD Vacuum Revealed by Overlap Fermions
• How Self-Dual is QCD?
• Shrinking fermionic modes, on the lattice and in the continuum
• Investigating the topological structure of quenched lattice QCD with overlap fermions by using multi-probing approximation
• Nonperturbative physics at short distances
• $\eta$ and ${\eta }^{\prime }$ mesons from $N_f=2+1$ lattice QCD at the physical point using topological charge operators