Magnetic monopole dominance for the Wilson loops in higher representations

TL;DR

This paper investigates magnetic monopole dominance in quark confinement by using a gauge-invariant lattice formulation and the non-Abelian Stokes theorem to analyze Wilson loops in higher representations, demonstrating the monopoles' dominant role.

Contribution

It introduces a gauge-invariant method to define magnetic monopoles and analyze their dominance in string tension for higher representations using the non-Abelian Stokes theorem.

Findings

Magnetic monopoles reproduce the correct string tension in higher representations.

The proposed gauge-invariant operators successfully demonstrate monopole dominance.

Numerical lattice simulations support the magnetic monopole's role in confinement.

Abstract

The dual superconductor picture is one of the most promising scenarios for quark confinement. To investigate this picture in a gauge-invariant manner, we have proposed a new formulation of Yang-Mills theory, named the decomposition method, on the lattice. The so-called restricted field obtained from the gauge-covariant decomposition plays the dominant role in quark confinement. It has been known by preceding works that the restricted-field dominance is not observed for the Wilson loop in higher representations if the restricted part of the Wilson loop is obtained by adopting the Abelian projection or the field decomposition naively in the same way as done in the fundamental representation. Recently, through the non-Abelian Stokes theorem (NAST) for the Wilson loop operator, we have proposed suitable gauge-invariant operators constructed from the restricted field to reproduce the correct behavior of the original Wilson loop averages for higher representations. We have demonstrated the numerical evidence for the restricted-field dominance in the string tension. In this talk, we focus on the magnetic monopole. According to this picture, magnetic monopoles causing the dual superconductivity are the dominant degrees of freedom responsible for confinement. With the help of the NAST, we define the magnetic monopole and the string tension extracted from the magnetic-monopole part of the Wilson loop in a gauge-invariant manner. We will further perform lattice simulations to measure the static potential for quarks in higher representations using the proposed operators and examine the magnetic monopole dominance in the string tension, which means that the string tension extracted from the magnetic-monopole part of the Wilson loop reproduces the proper string tension obtained from the original Wilson loop.