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Quark confinement: dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang-Mills theory
The purpose of this paper is to review the recent progress in understanding quark confinement. The emphasis of this review is placed on how to obtain a manifestly gauge-independent picture for quark
Compact lattice formulation of Cho–Faddeev–Niemi decomposition: String tension from magnetic monopoles
Abstract In this Letter we begin on a new lattice formulation of the non-linear change of variables called the Cho–Faddeev–Niemi decomposition in SU ( 2 ) Yang–Mills theory. This is a compact lattice
Lattice construction of Cho-Faddeev-Niemi decomposition and gauge invariant monopole
Abstract We present the first implementation of the Cho–Faddeev–Niemi decomposition of the SU(2) Yang–Mills field on a lattice. Our construction retains the color symmetry (global SU(2) gauge
Compact lattice formulation of Cho–Faddeev–Niemi decomposition: Gluon mass generation and infrared Abelian dominance
Abstract This Letter complements a new lattice formulation of SU(2) Yang–Mills theory written in terms of new variables in a compact form proposed in the previous paper. The new variables used in the
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
Non-Abelian Dual Superconductor Picture for Quark Confinement
We give a theoretical framework for defining and extracting non-Abelian magnetic monopoles in a gauge-invariant way in SU(N) Yang-Mills theory to study quark confinement. Then we give numerical
Type of dual superconductivity for the SU(2) Yang–Mills theory
We investigate the type of dual superconductivity responsible for quark confinement. For this purpose, we solve the field equations of the U(1) gauge-scalar model to obtain a single static vortex
Gauge-independent “Abelian” and magnetic-monopole dominance, and the dual Meissner effect in lattice SU(2) Yang-Mills theory
In the $SU(2)$ Yang-Mills theory on the four-dimensional Euclidean lattice, we confirm the gauge-independent "Abelian" dominance (or the restricted field dominance) and gauge-independent
A new description of lattice Yang-Mills theory and non-Abelian monopoles as the quark confiner
We propose a new description of the SU(N) Yang-Mills theory on a lattice, which enables one to explain quark confinement based on the dual superconductivity picture in a gauge independent way. This
Magnetic monopole versus vortex as gauge-invariant topological objects for quark confinement
First, we give a gauge-independent definition of chromomagnetic monopoles in $SU(N)$ Yang-Mills theory which is derived through a non-Abelian Stokes theorem for the Wilson loop operator. Then we