Laplacian modes probing gauge fields
arXiv:hep-lat/0509020 · doi:10.1103/PhysRevD.72.114502
Abstract
We show that low-lying eigenmodes of the Laplace operator are suitable to represent properties of the underlying SU(2) lattice configurations. We study this for the case of finite temperature background fields, yet in the confinement phase. For calorons as classical solutions put on the lattice, the lowest mode localizes one of the constituent monopoles by a maximum and the other one by a minimum, respectively. We introduce adjustable phase boundary conditions in the time direction, under which the role of the monopoles in the mode localization is interchanged. Similar hopping phenomena are observed for thermalized configurations. We also investigate periodic and antiperiodic modes of the adjoint Laplacian for comparison. In the second part we introduce a new Fourier-like low-pass filter method. It provides link variables by truncating a sum involving the Laplacian eigenmodes. The filter not only reproduces classical structures, but also preserves the confining potential for thermalized ensembles. We give a first characterization of the structures emerging from this procedure.
43 pages, 26 figures
References in corpus (18)
- Properties of the deconfining phase transition in SU(N) gauge theories
- Quantum weights of dyons and of instantons with non-trivial holonomy
- Propagators and running coupling from SU(2) lattice gauge theory
- Low-Dimensional Long-Range Topological Charge Structure in the QCD Vacuum
- New findings for topological excitations in SU(3) lattice gauge theory
- Higher charge calorons with non-trivial holonomy
- Localized eigenmodes of covariant Laplacians in the Yang-Mills vacuum
- Probing for Instanton Quarks with epsilon-Cooling
- Topological lumps and Dirac zero modes in SU(3) lattice gauge theory on the torus
- The monopole content of topological clusters : have KvB calorons been found?
- Searching for KvBLL calorons in SU(3) lattice gauge field ensembles
- Calorons in SU(3) lattice gauge theory
- The Analysis of Space-Time Structure in QCD Vacuum I: Localization vs Global Behavior in Local Observables and Dirac Eigenmodes
- Calorons with non-trivial holonomy on and off the lattice
- Adjoint modes as probes of gauge field structure
- Lower-dimension vacuum defects in lattice Yang-Mills theory
- Gauge Singularities in the SU(2) Vacuum on the Lattice
- On the zero of the fermion zero mode
Cited by in corpus (24)
- Theta dependence of SU(N) gauge theories in the presence of a topological term
- Linking confinement to spectral properties of the Dirac operator
- Vacuum structure revealed by over-improved stout-link smearing compared with the overlap analysis for quenched QCD
- Relation between chiral symmetry breaking and confinement in YM-theories
- Anderson localization through Polyakov loops: lattice evidence and Random matrix model
- Gauge-Invariant Formalism with a Dirac-mode Expansion for Confinement and Chiral Symmetry Breaking
- Chiral symmetry and spectral properties of the Dirac operator in G2 Yang-Mills Theory
- Quantitative comparison of filtering methods in lattice QCD
- Relation between Confinement and Chiral Symmetry Breaking in Temporally Odd-number Lattice QCD
- Topology of dynamical lattice configurations including results from dynamical overlap fermions
- The Vortex Structure of SU(2) Calorons
- Topology via Spectral Projectors with Staggered Fermions
- Lattice QCD analysis of the Polyakov loop in terms of Dirac eigenmodes
- Topological objects in QCD
- Peculiarities in the Spectrum of the Adjoint Scalar Kinetic Operator in Yang-Mills Theory
- Confinement from semiclassical gluon fields in SU(2) gauge theory
- Analytical Formulae of the Polyakov and the Wilson Loops with Dirac Eigenmodes in Lattice QCD
- Static quark-antiquark potential and Dirac eigenvector correlators
- Constructing static quark-anti-quark creation operators from Laplacian eigenmodes
- Ultraviolet filtering of lattice configurations and applications to Monte Carlo dynamics
- Topological zero modes at nonzero chemical potential
- Thin and dressed Polyakov loops from spectral sums of lattice differential operators
- Filtered topological structure of the QCD vacuum: Effects of dynamical quarks
- Exploring the QCD vacuum - (some) recent developments in confinement and topology