Wilson loop ($W_{\gamma }=\mathrm{tr}\mathcal{P}\exp (-{\oint }_{\gamma }A)$)

With gauge covariant derivative $D=d+A$, a Wilson loop is the matrix trace in a specified group representation of parallel transport around a closed curve. The holonomy of a connection changes by conjugation under gauge equivalence of principal connections, so its trace is gauge-invariant. It detects global connection data even when the local gauge curvature is zero.