Wilsonian effective action for SU(2) Yang-Mills theory with(2)

The Cho-Faddeev-Niemi-Shabanov decomposition of the SU(2) Yang-Mills field is employed for the calculation of the corresponding Wilsonian effective action to one-loop order with covariant gauge fixing. The generation of a mass scale is observed, and the fl

For the pure Yang-Mills(YM)sector of QCD,such a guess has recently been made by Faddeev and Niemi[1]inspired by the work of Cho[2].For the gauge group SU(2),they decomposed the(implicitly gauge-?xed)gauge potential Aµinto an“abelian”component Cµ,a unit color vector n and a complex scalar?eld?;here,Cµis the local projection of Aµonto some direction in color space de?ned by the space-dependent n.Faddeev and Niemi conjectured that the important low-energy dynamics of SU(2)YM theory1is determined by the n?eld;its e?ective action of nonlinear sigma-model type,the Skyrme-Faddeev model,should then arise from integrating out the further degrees of freedom:Cµ,?,...:

ΓFN e?= d4x m2(?µn)2+1

1Di?erent generalizations of the gauge?eld decomposition for higher gauge groups can be found in[3], [4]and[9].

2In a very recent paper[7],Faddeev and Niemi generalized their decomposition in order to obtain a manifest duality between the here-considered“magnetic”and additional“electric”variables,involving an abelian scalar multiplet with two complex scalars.This electric sector will not be considered in the present work.

3A di?erent approach was put forward in[8],where the n?eld was identi?ed by constructing an unconstraint version of SU(2)Yang-Mills theory in a Hamiltonian context.

2

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