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In previous works, we have proposed a new formulation of Yang-Mills theory onthe lattice so that the so-called restricted field obtained from thegauge-covariant decomposition plays the dominant role in quark confinement.This framework improves the Abelian projection in the gauge-independent manner.For quarks in the fundamental representation, we have demonstrated somenumerical evidences for the restricted field dominance in the string tension,which means that the string tension extracted from the restricted part of theWilson loop reproduces the string tension extracted from the original Wilsonloop. However, it is known that the restricted field dominance is not observedfor the Wilson loop in higher representations if the restricted part of theWilson loop is extracted by adopting the Abelian projection or the fielddecomposition naively in the same way as in the fundamental representation. Inthis paper, therefore, we focus on confinement of quarks in higherrepresentations. By virtue of the non-Abelian Stokes theorem for the Wilsonloop operator, we propose suitable gauge-invariant operators constructed fromthe restricted field to reproduce the correct behavior of the original Wilsonloop averages for higher representations. Moreover, we perform latticesimulations to measure the static potential for quarks in higherrepresentations using the proposed operators. We find that the proposedoperators well reproduce the behavior of the original Wilson loop average,namely, the linear part of the static potential with the correct value of thestring tension, which overcomes the problem that occurs in naively applyingAbelian-projection to the Wilson loop operator for higher representations.

How to extract the dominant part of the Wilson loop average in higher representations