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

Understand

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.