Confinement, chiral symmetry, and the lattice

Abstract

Two crucial properties of QCD, confinement and chiral symmetry breaking, cannot be understood within the context of conventional Feynman perturbation theory. Non-perturbative phenomena enter the theory in a fundamental way at both the classical and quantum level. Over the years a coherent qualitative picture of the interplay between chiral symmetry, quantum mechanical anomalies, and the lattice has emerged and is reviewed here.

126 pages, 36 figures. Revision corrects additional typos and renumbers equations to be more consistent with the published version

References in corpus (7)

• Creutz Fermions on an Orthogonal Lattice
• Classification of Minimally Doubled Fermions
• One flavor QCD
• Quantitative comparison of filtering methods in lattice QCD
• Effective potentials, thermodynamics, and twisted mass quarks
• Anomalies, gauge field topology, and the lattice
• Quark mass dependence of two-flavor QCD

Cited by in corpus (20)

• Parton distributions and lattice QCD calculations: a community white paper
• Scale-dependent mass anomalous dimension from Dirac eigenmodes
• An Analysis of Scheme Transformations in the Vicinity of an Infrared Fixed Point
• Scheme Transformations in the Vicinity of an Infrared Fixed Point
• Study of Scheme Transformations to Remove Higher-Loop Terms in the $\beta$ Function of a Gauge Theory
• Staggered fermions, zero modes, and flavor-singlet mesons
• Gauge-Invariant Formalism with a Dirac-mode Expansion for Confinement and Chiral Symmetry Breaking
• Chiral Symmetry Breaking on the Lattice
• Standard Model as the topological material
• Bounds on quantum gravity parameter from the $SU(2)$ NJL effective model of QCD
• Reducing the number of counterterms with new minimally doubled actions
• Strategies for quantum-optimized construction of interpolating operators in classical simulations of lattice quantum field theories
• Topological Aspects of Fermions on Hyperdiamond
• Analytical Formulae of the Polyakov and the Wilson Loops with Dirac Eigenmodes in Lattice QCD
• Quark masses, the Dashen phase, and gauge field topology
• New chiral lattice actions of the Borici-Creutz type
• On Flavor Symmetry in Lattice Quantum Chromodynamics
• Hydrodynamics and transport coefficients in an infrared-deformed soft-wall AdS/QCD model at finite temperature
• How Self-Dual is QCD?
• Phase structure with nonzero ${\Theta }_{\mathrm{QCD}}$ and twisted mass fermions