Topology of the SU(2) vacuum: a lattice study using improved cooling

Abstract

We study the topological structure of the SU(2) vacuum at zero temperature: topological susceptibility, size, shape and distance distributions of the instantons. We use a cooling algorithm based on an improved action with scale invariant instanton solutions. This algorithm needs no monitoring or calibration, has an inherent cut off for dislocations and leaves unchanged instantons at physical scales. The physical relevance of our results is checked by studying the scaling and finite volume dependence. We obtain a susceptibility of (200(15) MeV)^4. The instanton size distribution is peaked around 0.43fm, and the distance distribution indicates a homogeneous, random spatial structure.

45 pages, Latex, 19 figures. Improvements and some new remarks added in sections 3.4, 3.5, 4. and figures 14, 16, 17 and 18 (concerning mostly I-A interactions and density-density correlations). New references added

Cited by in corpus (105)

• Full nonperturbative QCD simulations with 2+1 flavors of improved staggered quarks
• Domain wall QCD with physical quark masses
• Instantons at work
• Physical Results from 2+1 Flavor Domain Wall QCD and SU(2) Chiral Perturbation Theory
• Continuum Limit Physics from 2+1 Flavor Domain Wall QCD
• On the relevance of center vortices to QCD
• Theta dependence of SU(N) gauge theories in the presence of a topological term
• The chiral transition and U(1)_A symmetry restoration from lattice QCD using Domain Wall Fermions
• Domain Wall QCD with Near-Physical Pions
• Highly-improved lattice field-strength tensor
• Hadron Masses From Novel Fat-Link Fermion Actions
• Topological Structure of the SU(3) Vacuum
• Instantons, the QCD Vacuum, and Hadronic Physics
• Problems in Lattice Gauge Fixing
• Off-equilibrium sphaleron transitions in the Glasma
• Direct instantons, topological charge screening and QCD glueball sum rules
• The U_A(1) Problem on the Lattice with Ginsparg-Wilson Fermions
• The QCD vacuum
• The Low Energy Constants of $SU(2)$ Partially Quenched Chiral Perturbation Theory from $N_f=2+1$ Domain Wall QCD
• Instantons and $<A^2>$ Condensate
• The strong coupling constant at small momentum as an instanton detector
• Topological charge using cooling and the gradient flow
• Revealing Topological Structure in the SU(2) Vacuum
• The Low-Lying Dirac Spectrum of Staggered Quarks
• Instanton-Induced Cross-Sections in Deep-Inelastic Scattering
• The hermitian Wilson-Dirac operator in smooth SU(2) instanton backgrounds
• Vacuum structure revealed by over-improved stout-link smearing compared with the overlap analysis for quenched QCD
• A comprehensive picture of topological excitations in finite temperature lattice QCD
• Calibration of Smearing and Cooling Algorithms in SU(3)-Color Gauge Theory
• Cooling, Physical Scales and Topology
• First results from 2+1-Flavor Domain Wall QCD: Mass Spectrum, Topology Change and Chiral Symmetry with $L_s=8$
• A Model for QCD at High Density and Large Quark Mass
• ${\eta }^{\prime }$ meson mass from topological charge density correlator in QCD
• Improved Smoothing Algorithms for Lattice Gauge Theory
• General Algorithm For Improved Lattice Actions on Parallel Computing Architectures
• Multiscale Monte Carlo equilibration: Pure Yang-Mills theory
• Topological susceptibility from the overlap
• Topological susceptibility with the improved Asqtad action
• Neutron and proton electric dipole moments from $N_f=2+1$ domain-wall fermion lattice QCD
• Topological susceptibility of pure gauge theory using Density of States
• Topology of full QCD
• A critical comparison of different definitions of topological charge on the lattice
• On the spectrum of the Wilson-Dirac lattice operator in topologically non-trivial background configurations
• The monopole content of topological clusters : have KvB calorons been found?
• The Euclidean two-point correlation function of the topological charge density
• A Chiral Solution to the Ginsparg-Wilson Equation
• Diffusion of topological charge in lattice QCD simulations
• 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
• Peeking into the $\theta$ vacuum
• Local topological and chiral properties of QCD
• Gluon Green functions free of Quantum fluctuations
• Accessing the topological susceptibility via the Gribov horizon
• Non-Abelian chiral instabilities at high temperature on the lattice
• Measuring the Topological Susceptibility in a Fixed Sector
• Clover improvement, spectrum and Atiyah-Singer index theorem for the Dirac operator on the lattice
• Comments on the Instanton Size Distribution
• Twist-4 contribution to unpolarized structure functions F_L and F_2 from instantons
• SU(2) Gluodynamics and HP1 sigma-model embedding: Scaling, Topology and Confinement
• Interpreting Numerical Measurements in Fixed Topological Sectors
• Is $N=2$ Large?
• Cooling for instantons and the Wrath of Nahm
• Numerical study of lattice index theorem usingimproved cooling and overlap fermions
• Domain wall fermion zero modes on classical topological backgrounds
• Low-lying eigenmodes of the Wilson-Dirac operator and correlations with topological objects
• Domain Wall Fermion QCD with the Exact One Flavor Algorithm
• Confinement from semiclassical gluon fields in SU(2) gauge theory
• Noisy Monte Carlo revisited
• Monopole characteristics in various Abelian gauges
• Instantons and Chiral Symmetry on the Lattice
• Instanton contribution to scalar charmonium and glueball decays
• Infrared degrees of freedom of Yang-Mills theory in the Schroedinger representation
• Comparison of |Q|=1 and |Q|=2 gauge-field configurations on the lattice four-torus
• Temperature dependence of instantons in QCD
• Topological susceptibility in SU(2) Yang-Mills theory in the Hamiltonian approach in Coulomb gauge
• Light Quark Mass Reweighting
• Multiscale Monte Carlo equilibration: Two-color QCD with two fermion flavors
• Laplacian gauge and instantons
• Topological features of the deconfinement transition
• Monopole Clustering and Color Confinement in the Multi-Instanton System
• On the spectral density from instantons in quenched QCD
• Novel fat-link fermion actions
• Lattice Gauge Fields Topology Uncovered by Quaternionic sigma-model Embedding
• Instanton classical solutions of SU(3) fixed point actions on open lattices
• $\theta$ dependence of $T_c$ in 4d SU(3) Yang-Mills theory with histogram method and the Lee-Yang zeros in the large $N$ limit
• Ultraviolet filtering of lattice configurations and applications to Monte Carlo dynamics
• Topological Susceptibility and Zero Mode Size in Lattice QCD
• Glueballs and topology with O(a)-improved lattice QCD
• Topological charge and cooling scales in pure SU(2) lattice gauge theory
• Proposal for Topologically Unquenched QCD
• Numerical evidence for fractional topological objects in SU(3) gauge theory
• Gauge Singularities in the SU(2) Vacuum on the Lattice
• Understanding the U(1) problem through dyon configuration in the Abelian projection
• Hadron Properties with FLIC Fermions
• Topological observables and $\theta$ dependence in high temperature QCD from lattice simulations
• Chiral symmetry and taste symmetry from the eigenvalue spectrum of staggered Dirac operators
• The $U_A(1)$ Problem on the Lattice
• Vacuum structure and string tension in Yang-Mills dimeron ensembles
• Finite Temperature QCD on Anisotropic Lattices
• QCD topology using scale controlled cooling: Densities and cooling invariant observables
• Analyzing the spectrum of general, non-hermitian Dirac operators
• Topology without cooling: instantons and monopoles near to deconfinement
• Cooling, Physical Scales and the Vacuum Structure of Y-M Theories
• Dynamical suppression of large instantons
• Heavy-light quark systems from the QCD instanton vacuum: $N_f=1$ light flavor case