Reformulating SU(N) Yang-Mills theory based on change of variables

Abstract

We propose a new version of SU(N) Yang-Mills theory reformulated in terms of new field variables which are obtained by a nonlinear change of variables from the original Yang-Mills gauge field. The reformulated Yang-Mills theory enables us to study the low-energy dynamics by explicitly extracting the topological degrees of freedom such as magnetic monopoles and vortices to clarify the mechanism for quark confinement. The dual superconductivity in Yang-Mills theory is understood in a gauge-invariant manner, as demonstrated recently by a non-Abelian Stokes theorem for the Wilson loop operator, although the basic idea of this reformulation is based on the Cho-Faddeev-Niemi decomposition of the gauge potential.

51 pages, 1 figure; version to be published in Prog. Theor. Phys. Vol. 120, No.1 (2008)

References in corpus (5)

• 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
• New descriptions of lattice SU(N) Yang-Mills theory towards quark confinement
• 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 (30)

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• Impact of the strong electromagnetic field on the QCD effective potential for homogeneous Abelian gluon field configurations
• New descriptions of lattice SU(N) Yang-Mills theory towards quark confinement
• Non-Abelian Dual Superconductor Picture for Quark Confinement
• Exact vortex solutions in a CP^N Skyrme-Faddeev type model
• Center vortices as sources of Abelian dominance in pure SU(2) Yang-Mills theory
• Domain wall network as QCD vacuum and the chromomagnetic trap formation under extreme conditions
• Non-Abelian dual superconductivity in SU(3) Yang-Mills theory: dual Meissner effect and type of the vacuum
• Magnetic monopoles and center vortices as gauge-invariant topological defects simultaneously responsible for confinement
• The exact decomposition of gauge variables in lattice Yang-Mills theory
• Gauge-independent "Abelian" and magnetic-monopole dominance, and the dual Meissner effect in lattice $SU(2)$ Yang-Mills theory
• Gauge-independent Brout-Englert-Higgs mechanism and Yang-Mills theory with a gauge-invariant gluon mass term
• Weyl group, CP and the kink-like field configurations in the effective SU(3) gauge theory
• $SU(3)$ Knot Solitons: Hopfions in the $F_2$ Skyrme-Faddeev-Niemi model
• BPS Sphalerons in the $F_2$ Non-Linear Sigma Model
• Some properties of (3+1) dimensional vortex solutions in the extended CP^N Skyrme-Faddeev model
• Magnetic Monopole Loops supported by a Meron pair as the Quark Confiner
• Magnetic monopoles in pure $SU(2)$ Yang--Mills theory with a gauge-invariant mass
• How to get rid of Dirac worldsheets in the Cho-Fadeev-Niemi representation of SU(2) Yang-Mills theory
• Jackiw-Nohl-Rebbi two-instanton as a source of magnetic monopole loop
• Domain walls and gauge field localization in strongly-coupled pure Yang-Mills theories
• Composite operator and condensate in the $SU(N)$ Yang-Mills theory with $U(N-1)$ stability group
• Gauge-covariant decomposition and magnetic monopole for G(2) Yang-Mills field
• Introducing vortices in the continuum using direct and indirect methods
• How to extract the dominant part of the Wilson loop average in higher representations
• Direct and Indirect Methods of Vortex Identification in Continuum limit
• 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