On Some Features of Color Confinement

TL;DR

This paper proposes that a dual symmetry related to non-trivial spatial homotopy explains color confinement, emphasizing the role of magnetic monopoles, the 't Hooft tensor, and dual superconductivity mechanisms in quantum chromodynamics.

Contribution

It introduces a dual symmetry framework based on homotopy theory to explain color confinement and derives the general form of the 't Hooft tensor applicable to any gauge group.

Findings

Dual symmetry explains confinement consistent with lattice data

Magnetic charge is the only relevant dual quantum number

Derived the general form of the 't Hooft tensor for gauge groups

Abstract

It is argued that a dual symmetry is needed to naturally explain experimental limits on color confinement. Since color is an exact symmetry the only possibility is that this symmetry be a dual symmetry, related to non trivial spatial homotopy. The sphere at infinity of 3-dimensional space being 2-dimensional, the relevant homotopy is $\Pi_2$, the corresponding configurations monopoles, and the mechanism dual superconductivity. The consistency of the order-disorder nature of the deconfining transition is compared with lattice data . It is also shown that the only dual quantum number is magnetic charge and the key quantity is 't Hooft tensor, independent of the gauge group. The general form of the 't Hooft tensor is computed.