QCD Topology at Finite Temperature: Statistical Mechanics of Selfdual Dyons

Abstract

Topological phenomena in gauge theories have long been recognized as the driving force for chiral symmetry breaking and confinement. These phenomena can be conveniently investigated in the semi-classical picture, in which the topological charge is entirely carried by (anti-)self-dual gauge configurations. In such an approach, it has been shown that near the critical temperature, the non-zero expectation value of the Polyakov loop (holonomy) triggers the "Higgsing" of the color group, generating the splitting of instantons into $N_c$ self-dual dyons. A number of lattice simulations have provided some evidence for such dyons, and traced their relation with specific observables, such as the Dirac eigenvalue spectrum. In this work, we formulate a model, based on one-loop partition function and including Coulomb interaction, screening and fermion zee modes. We then perform the first numerical Monte Carlo simulations of a statistical ensemble of self-dual dyons,as a function of their density, quark mass and the number of flavors. We study different dyonic two-point correlation functions and we compute the Dirac spectrum, as a function of the ensemble diluteness and the number of quark flavors.

arXiv commentv2 has minor changes and one ref added

References in corpus (24)

• Instantons in QCD
• Random matrix theory and spectral sum rules for the Dirac operator in QCD
• Monopole Constituents inside SU(n) Calorons
• Monopoles and Instantons on Partially Compactified D-Branes
• Quantum weights of dyons and of instantons with non-trivial holonomy
• Topology and confinement
• Testing the self-duality of topological lumps in SU(3) lattice gauge theory
• Gauge invariant structures and Confinement
• The dyonic picture of topological objects in the deconfined phase
• Do classical configurations produce Confinement?
• The Chiral Symmetry Breaking/Restoration in Dyonic Vacuum
• Are There Diquarks in the Nucleon?
• Instanton Contribution to the Pion Electro-Magnetic Formfactor at Q^2 > 1 GeV^2
• Calorons and monopoles from smeared SU(2) lattice fields at non-zero temperature
• Free energy for parameterized Polyakov loops in SU(2) and SU(3) lattice gauge theory
• Exploring the Chiral Regime of QCD in the Interacting Instanton Liquid Model
• Instantons, diquarks and non-leptonic weak decays of hyperons
• Proton Electro-Magnetic Form-Factors in the Instanton Liquid Model
• Instanton Contribution to the Proton and Neutron Electric Form Factors
• Instanton Contribution to the Electro-Magnetic Form Factors of the Nucleon
• Parameter free calculation of hadronic masses from instantons
• Instantons, Chiral Dynamics and Hadronic Resonances
• Instantons and the $\Delta I=1/2$ Rule
• Effects of the low lying Dirac modes on excited hadrons in lattice QCD

Cited by in corpus (28)

• Deconfinement and continuity between thermal and (super) Yang-Mills theory for all gauge groups
• Confining Dyon-Anti-Dyon Coulomb Liquid Model I
• Light Quarks in the Screened Dyon-Anti-Dyon Coulomb Liquid Model II
• (S)QCD on R^3 x S^1: Screening of Polyakov loop by fundamental quarks and the demise of semi-classics
• Interacting Ensemble of the Instanton-dyons and Deconfinement Phase Transition in the SU(2) Gauge Theory
• Instanton-dyon Ensemble with two Dynamical Quarks: the Chiral Symmetry Breaking
• The localization transition in SU(3) gauge theory
• Topology across the finite temperature transition studied by overimproved cooling in gluodynamics and QCD
• Dyons near the transition temperature in lattice QCD
• Classical interactions of the instanton-dyons with antidyons
• The Instanton-Dyon Liquid Model V: Twisted Light Quarks
• Dynamical de Sitter phase and nontrivial holonomy in strongly coupled gauge theories in expanding Universe
• The Instanton-Dyon Liquid Model III: Finite Chemical Potential
• Dyon structures in the deconfinement phase of lattice gluodynamics: topological clusters, holonomies and Abelian monopoles
• Conformal window in QCD for large numbers of colours and flavours
• Confinement, Holonomy and Correlated Instanton-Dyon Ensemble I: SU(2) Yang-Mills Theory
• Light Adjoint Quarks in the Instanton-Dyon Liquid Model IV
• Spontaneous symmetry breaking, and strings defects in hypercomplex gauge field theories
• Dyons and Roberge - Weiss transition in lattice QCD
• Lectures on nonperturbative QCD ( Nonperturbative Topological Phenomena in QCD and Related Theories)
• On Chiral Symmetry Breaking, Topology and Confinement
• Dense Instanton-Dyon Liquid Model: Diagrammatics
• Hadronic Correlation Functions in the Random Instanton-dyon Ensemble
• Confinement from Correlated Instanton-Dyon Ensemble in SU(2) Yang-Mills Theory
• Recent progress in understanding deconfinement and chiral restoration phase transitions
• Dyons near the transition temperature in $SU(3)$ lattice gluodynamics
• Density and correlations of topological objects near the transition temperature in lattice gluodynamics
• Knot topology in QCD