New descriptions of lattice SU(N) Yang-Mills theory towards quark confinement

Abstract

We give new descriptions of lattice SU(N) Yang-Mills theory in terms of new lattice variables. The validity of such descriptions has already been demonstrated in the SU(2) Yang-Mills theory by our previous works from the viewpoint of defining and extracting topological degrees of freedom such as gauge-invariant magnetic monopoles and vortices which play the dominant role in quark confinement. In particular, we have found that the SU(3) lattice Yang-Mills theory has two possible options, maximal and minimal: The existence of the minimal option has been overlooked so far, while the maximal option reproduces the conventional SU(3) Cho-Faddeev-Niemi-Shabanov decomposition in the naive continuum limit. The new description gives an important framework for understanding the mechanism of quark confinement based on the dual superconductivity.

Cover+18 pages, 1 figure; version to appear in Phys. Lett. B

References in corpus (8)

• Spin-Charge Separation, Conformal Covariance and the SU(2) Yang-Mills Theory
• Gauge-invariant gluon mass, infrared Abelian dominance and stability of magnetic vacuum
• Reformulating SU(N) Yang-Mills theory based on change of variables
• Compact lattice formulation of Cho-Faddeev-Niemi decomposition: gluon mass generation and infrared Abelian dominance
• Wilson loop and magnetic monopole through a non-Abelian Stokes theorem
• Compact lattice formulation of Cho-Faddeev-Niemi decomposition: string tension from magnetic monopoles
• Magnetic monopoles and center vortices as gauge-invariant topological defects simultaneously responsible for confinement
• Proving Abelian dominance in the Wilson loop operator

Cited by in corpus (13)

• Quark confinement: dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang-Mills theory
• Reformulating SU(N) Yang-Mills theory based on change of variables
• Non-Abelian Dual Superconductor Picture for Quark Confinement
• Gauge-independent "Abelian" and magnetic-monopole dominance, and the dual Meissner effect in lattice $SU(2)$ Yang-Mills theory
• Magnetic monopoles and center vortices as gauge-invariant topological defects simultaneously responsible for confinement
• Magnetic Monopole Loops supported by a Meron pair as the Quark Confiner
• Derivation of Dielectric Model of Confinement in QCD
• Gauge-independent transition separating confinement and Higgs phases in lattice SU(2) gauge theory with a scalar field in the fundamental representation
• Experimental Verification of Two types of Gluon Jets in QCD
• How to extract the dominant part of the Wilson loop average in higher representations
• 2D discrete Yang-Mills equations on the torus
• Discriminating between two reformulations of SU(3) Yang-Mills theory on a lattice
• Reformulations of the Yang-Mills theory toward quark confinement and mass gap