Magnetic monopoles and center vortices as gauge-invariant topological defects simultaneously responsible for confinement

TL;DR

This paper introduces a gauge-invariant framework for defining vortex surfaces and magnetic monopoles in SU(N) Yang-Mills theory, demonstrating their combined role in quark confinement without gauge fixing.

Contribution

It presents a gauge-invariant method to define vortex surfaces and magnetic monopoles, showing their joint responsibility for confinement in four-dimensional spacetime.

Findings

Gauge-invariant magnetic monopoles with fractional charges emerge at vortex boundaries.

The asymptotic string tension depends on N-ality, matching theoretical expectations.

Magnetic monopoles and vortices are both essential for confinement, as shown via the Wilson criterion.

Abstract

We give a gauge-invariant definition of the vortex surface in SU(N) Yang-Mills theory without using the gauge fixing procedure. In this construction, gauge-invariant magnetic monopoles with fractional magnetic charges emerge in the boundary of the non-oriented vortex surface such that the asymptotic string tension reproduces the correct $N$-ality dependence. We show that gauge-invariant magnetic monopoles and vortices are simultaneously responsible for quark confinement in four dimensional spacetime based on the Wilson criterion. These results are extracted from a non-Abelian Stokes theorem derived in the previous paper.