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

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

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Wilsonian e?ective action for SU(2)Yang-Mills theory with Cho-Faddeev-Niemi-Shabanov decomposition Holger Gies ?Institut f¨u r theoretische Physik,Universit¨a t T¨u bingen,D-72076T¨u bingen,Germany and Theory Division,CERN,CH-1211Geneva,Switzerland E-mail:holger.gies@cern.ch February 1,2008Abstract The Cho-Faddeev-Niemi-Shabanov decomposition of the SU(2)Yang-Mills ?eld is employed for the calculation of the corresponding Wilsonian e?ective action to one-loop order with covariant gauge ?xing.The generation of a mass scale is observed,and the ?ow of the marginal couplings is studied.Our results indicate that higher-derivative terms of the color-unit-vector n ?eld are necessary for the description of topologically stable knotlike solitons which have been conjectured to be the large-distance degrees of freedom.

1Introduction

The fact that quarks and gluons are not observed as asymptotic states in our world indicates that a description in terms of these ?elds is not the most appropriate language for discussing low-energy QCD.On the other hand,there seems to be little predictive virtue in describing the low-energy domain only by observable quantities,such as mesons and baryons.A purposive procedure can be the identi?cation of those (not necessarily observable)degrees of freedom of the system that allow for a “simple”description of the observable states.The required “simplicity”can be measured in terms of the simplicity of the action that governs those degrees of freedom.Clearly,a clever guess of such degrees of freedom is halfway to the solution of the theory;the remaining problem is to prove that these degrees of freedom truly arise from the fundamental theory by integrating out the high-energy modes.

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