# Confinement of quarks in higher representations in view of dual superconductivity

## TL;DR

This paper advances the dual superconductor model of quark confinement by developing new lattice operators that accurately reproduce Wilson loop behavior in higher quark representations, overcoming previous limitations of Abelian projection methods.

## Contribution

It introduces operators constructed from the restricted field that correctly reproduce Wilson loops in higher representations, improving the gauge-independent approach to quark confinement.

## Key findings

- Proposed operators reproduce the Wilson loop behavior in higher representations.
- Lattice simulations confirm the effectiveness of the new operators.
- Overcomes limitations of naive Abelian projection in higher representations.

## Abstract

Dual superconductor picture is one of the most promising scenarios for quark confinement. We have proposed a new formulation of Yang-Mills theory on the lattice so that the so-called restricted field obtained from the gauge-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 some numerical evidences for the dual superconductivity. However, it is known that the expected behavior of the Wilson loop in higher representations cannot be reproduced if the restricted part of the Wilson loop is extracted by adopting the Abelian projection or the field decomposition naively in the same way as in the fundamental representation. In this talk, therefore, we focus on confinement of quarks in higher representations. By virtue of the non-Abelian Stokes theorem for the Wilson loop operator, we propose suitable operators constructed from the restricted field only in the fundamental representation to reproduce the correct behavior of the original Wilson loop in higher representations. Moreover, we perform lattice simulations to measure the static potential for quarks in higher representations using the proposed operators. We find that the proposed operators well reproduce the expected behavior of the original Wilson loop average, which overcomes the problem that occurs in naively applying Abelian-projection to the Wilson loop operator for higher representations.