Simplicity of confinement in SU(3) Yang-Mills theory

TL;DR

This paper introduces a new topological observable called 'simplicity' based on Abelian monopole currents in SU(3) Yang-Mills theory, which helps identify the deconfinement transition with higher precision.

Contribution

The paper proposes a novel topological measure, 'simplicity,' derived from monopole current graphs, providing a new way to study confinement and deconfinement in lattice gauge theories.

Findings

The simplicity observable accurately determines the deconfinement temperature.

Abelian current loops are strongly linked to confinement-related degrees of freedom.

The method offers improved precision over traditional techniques for phase transition detection.

Abstract

We introduce a novel observable associated to Abelian monopole currents defined in the Maximal Abelian Projection of SU(3) Yang-Mills theory that captures the topology of the current loop. This observable, referred to as the $\textit{simplicity}$, is defined as the ratio of the zeroth over the first Betti number of the current graph for a given field configuration. A numerical study of the expectation value of the simplicity performed in the framework of Lattice Gauge Theories enables us to determine the deconfinement temperature to a higher degree of accuracy than that reached by conventional methods at a comparable computational effort. Our results suggest that Abelian current loops are strongly correlated with the degrees of freedoms of the theory that determine confinement. Our investigation opens new perspectives for the definition of an order parameter for deconfinement in Quantum Chromodynamics able to expose the potentially rich phase structure of the theory.