The Confinement Problem in Lattice Gauge Theory

Abstract

I review investigations of the quark confinement mechanism that have been carried out in the framework of SU(N) lattice gauge theory. The special role of Z(N) center symmetry is emphasized.

104 pages. Invited review article for Progress of Particle and Nuclear Physics. v2: References added, minor revisions

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• QCD forces and heavy quark bound states
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• Dynamics of $SU(N)$ Supersymmetric Gauge Theory
• On the relevance of center vortices to QCD
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• Center Projection Vortices in Continuum Yang-Mills Theory
• A study of the 't Hooft loop in SU(2) Yang-Mills theory
• Renormalization group flow of SU(3) lattice gauge theory - Numerical studies in a two coupling space
• Center Vortices and Monopoles without lattice Gribov copies
• Gauge Fixing on the Lattice without Ambiguity
• Center vortices of Yang-Mills theory at finite temperatures
• Probing the QCD Vacuum with Static Sources in Maximal Abelian Projection
• Vortex Structure vs. Monopole Dominance in Abelian-Projected Gauge Theory
• Topology of Center Vortices
• Center vortex model for the infrared sector of Yang-Mills theory - Confinement and Deconfinement
• Center vortex model for the infrared sector of Yang-Mills theory - Topological Susceptibility
• Colour confinement as dual Meissner effect: $SU(2)$ gauge theory
• Computation of the Vortex Free Energy in SU(2) Gauge Theory
• Detecting Dual Superconductivity in the Ground State of Gauge Theory
• Spectrum of confining strings in SU(N) gauge theories
• Testing perturbation theory on the nf=0 static quark potential
• Confinement studies in lattice QCD
• Gluon Chain Model of the Confining Force
• The Role of Center Vortices in QCD
• The Structure of Projected Center Vortices in Lattice Gauge Theory
• Adjoint string breaking in 4d SU(2) Yang-Mills theory
• Center vortex model for the infrared sector of Yang-Mills theory - Quenched Dirac spectrum and chiral condensate
• P-vortices and Drama of Gribov Copies
• Scaling and Topological Charge of a Fixed Point Action for $SU(2)$ Gauge Theory
• Quantum fluctuations of Wilson loops from string models
• Direct Laplacian Center Gauge
• On P-vortices and the Gribov problem
• Center Disorder in the 3D Georgi-Glashow Model
• First Evidence for Center Dominance in SU(3) Lattice Gauge Theory
• The Maximal Abelian Gauge, Monopoles, and Vortices in SU(3) Lattice Gauge Theory
• Potentials between static SU(3) sources in the fat-center-vortices model
• The Vortex-Finding Property of Maximal Center (and Other) Gauges
• Center Projection With and Without Gauge Fixing
• New fixed point action for SU(3) lattice gauge theory
• Vortices, monopoles and confinement
• Vortices and confinement in hot and cold D=2+1 gauge theories
• Abelian Monopoles in SU(2) Lattice Gauge Theory as Physical Objects
• P-vortices, nexuses and effects of gauge copies
• P-Vortices, Gauge Copies, and Lattice Size
• k-String Tensions and Center Vortices at Large N
• Center vortex properties in the Laplace center gauge of SU(2) Yang-Mills theory
• Non-universal corrections to the tension ratios in softly broken N=2 SU(N) gauge theory
• Phases and Residual Gauge Symmetries of Higgs Models
• A Magnetic Monopole in Pure SU(2) Gauge Theory
• What are the Confining Field Configurations of Strong-Coupling Lattice Gauge Theory?
• Broadening of the QCD3 flux tube from the AdS/CFT correspondence
• Absence of confinement in the absence of vortices
• Ehrenfest theorems and charge antiscreening in Abelian projected gauge theories

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