Correct way to extract dominant part of the Wilson loop in higher representations

TL;DR

This paper proposes a redefinition of the Abelian Wilson loop to accurately extract the dominant part of the Wilson loop in higher representations, demonstrating Abelian dominance in lattice simulations for specific $SU(3)$ representations.

Contribution

It introduces a new method to redefine the Abelian Wilson loop, enabling correct extraction of dominant contributions in higher representations.

Findings

Redefinition of Abelian Wilson loop improves accuracy

Demonstrates Abelian dominance in adjoint and sextet representations

Validates the method with lattice simulation results

Abstract

The Abelian dominance for the string tension was shown for the fundamental sources in MA gauge in the lattice simulations. For higher representations, however, it is also known that the naive "Abelian" Wilson loop, which is defined by using the diagonal part of the gauge field, does not reproduce the correct behavior. To solve this problem, for an arbitrary representation of an arbitrary compact gauge group, we propose to redefine the "Abelian" Wilson loop. By using this redefined operator, we demonstrate the "Abelian" dominance for sources in the adjoint representation and the sextet representation of $SU(3)$ gauge group in lattice simulations.