# Abelian dominance and adjoint sources in lattice QCD

## TL;DR

This paper investigates how abelian dominance in lattice QCD extends from fundamental quarks to adjoint sources, providing theoretical derivations and numerical evidence supporting the reproduction of string tensions via abelian Wilson loops.

## Contribution

It demonstrates that abelian dominance applies to higher representations in lattice QCD and clarifies differences between projection methods with supporting numerical data.

## Key findings

- Fundamental and adjoint string tensions are reproduced by abelian Wilson loops.
- Abelian dominance extends to higher representations beyond fundamental quarks.
- Numerical evidence supports the extension of abelian dominance to adjoint sources.

## Abstract

Certain properties of maximal abelian projection are derived which suggest that the fundamental and adjoint SU(2) string tensions are reproduced by singly and doubly charged abelian Wilson loops, respectively. Thus, abelian dominance, which has been observed for color sources (quarks) in the fundamental representation, can be extended to higher representations. Numerical evidence in support of this conjecture also for adjoint quarks is presented. The difference between maximal abelian and local projections is elucidated and the role of non-Wilson-like terms in the effective abelian action is discussed.