The exact decomposition of gauge variables in lattice Yang-Mills theory

Abstract

In this paper, we consider lattice versions of the decomposition of the Yang- Mills field a la Cho-Faddeev-Niemi, which was extended by Kondo, Shinohara and Murakami in the continuum formulation. For the SU(N) gauge group, we propose a set of defining equations for specifying the decomposition of the gauge link variable and solve them exactly without using the ansatz adopted in the previous studies for SU(2) and SU(3). As a result, we obtain the general form of the decomposition for SU(N) gauge link variables and confirm the previous results obtained for SU(2) and SU(3).

16 pages

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
• New descriptions of lattice SU(N) Yang-Mills theory towards quark confinement
• Proving Abelian dominance in the Wilson loop operator

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