Some remarks on Abelian dominance∗

We used a renormalisation group based smoothing to address two questions related to Abelian dominance. Smoothing enabled us to extract the Abelian heavy-quark potential from time-like Wilson loops on Polyakov gauge projected configurations. We obtained a very small string tension which is inconsistent with the string tension extracted from Polyakov loop correlators. This shows that the Polyakov gauge projected Abelian configurations do not have a consistent physical meaning. We also applied the smoothing on SU(2) configurations to test how sensitive Abelian dominance in the maximal Abelian gauge is to the short distance fluctuations. We found that on smoothed SU(2) configurations the Abelian string tension was about 30% smaller than the SU(2) string tension which was unaffected by smoothing. This suggests that the approximate Abelian dominance found with the Wilson action is probably an accident and it has no fundamental physical relevance.