Localized eigenmodes of covariant Laplacians in the Yang-Mills vacuum

Abstract

As a probe of the Yang-Mills vacuum, we study numerically the eigenmode spectrum of the covariant lattice Laplacian operator. We find that the eigenmodes at the low and high ends of the spectrum are localized in finite regions whose volume is insensitive to the lattice volume. We also find that the vacuum is seen very differently by localized modes of the covariant Laplacian in different representations of the gauge group. In the fundamental representation, the data suggests that the localization volume is finite in physical units set by the string tension, and localization disappears when center vortices are removed. In the adjoint and j=3/2 representations the low and high-lying modes are far more localized, and the localization volume appears to scale to zero, in physical units, in the continuum limit. The adjoint Laplacian is insensitive to vortex removal, but we find that exponential localization is absent for adjoint eigenmodes in the Higgs phase of a gauge-Higgs theory. Localization is also absent in the spectrum of the Coulomb gauge Faddeev-Popov operator, as required in Coulomb gauge confinement scenarios.

arXiv comment11 pages, 24 figures, reference added

References in corpus (15)

• Variants of fattening and flavor symmetry restoration
• On the relevance of center vortices to QCD
• Coulomb Energy, Remnant Symmetry, and the Phases of Non-Abelian Gauge Theories
• Coulomb Energy, Vortices, and Confinement
• Center Vortices and Monopoles without lattice Gribov copies
• Gauge Fixing on the Lattice without Ambiguity
• Localization in Lattice QCD
• Fine tuned vortices in lattice SU(2) gluodynamics
• Direct Laplacian Center Gauge
• Mobility edge in lattice QCD
• Laplacian Abelian Projection
• Low-dimensional long-range topological structure in the QCD vacuum
• The Analysis of Space-Time Structure in QCD Vacuum I: Localization vs Global Behavior in Local Observables and Dirac Eigenmodes
• Lower-dimension vacuum defects in lattice Yang-Mills theory
• Vortices in the SU(2)-Higgs model -- Vortices and the covariant adjoint Laplacian

Cited by in corpus (22)

• Linking confinement to spectral properties of the Dirac operator
• Exploring the structure of the quenched QCD vacuum with overlap fermions
• Center Vortices and the Dirac Spectrum
• Closed k-strings in SU(N) gauge theories : 2+1 dimensions
• Anderson transition and multifractals in the spectrum of the Dirac operator of Quantum Chromodynamics at high temperature
• On the spectrum of the Faddeev-Popov operator in topological background fields
• Laplacian modes probing gauge fields
• Localization of Dirac Fermions in Finite-Temperature Gauge Theory
• Evidence for fine tuning of fermionic modes in lattice gluodynamics
• Optimising creation operators for charmonium spectroscopy on the lattice
• Anderson localization in QCD-like theories
• SU(2) Gluodynamics and HP1 sigma-model embedding: Scaling, Topology and Confinement
• Peculiarities in the Spectrum of the Adjoint Scalar Kinetic Operator in Yang-Mills Theory
• The factorisation of glue and mass terms in SU(N) gauge theories
• Lattice QCD analysis for Faddeev-Popov eigenmodes in terms of gluonic momentum components in the Coulomb gauge
• Localization of Low Lying Eigenmodes for Chirally Symmetric Dirac Operator
• Constructing static quark-anti-quark creation operators from Laplacian eigenmodes
• Laplacian modes as a filter
• Metal or Insulator? Dirac operator spectrum in holographic QCD
• Shrinking fermionic modes, on the lattice and in the continuum
• The determination of potential scales in 2+1 flavor QCD
• Tensor supercurrent in QCD