Why is it interesting?

Instead of using gauge potentials one can describe gauge fields also using Wilson lines. In contrast to gauge potentials, Wilson loops are completely gauge invariant.

The formulation of Yang-Mills theory which makes use of Wilson loops is called loop formulation.

Layman

The confining phase is usually defined by the behavior of the action of the Wilson loop, which is simply the path in spacetime traced out by a quark–antiquark pair created at one point and annihilated at another point. In a non-confining theory, the action of such a loop is proportional to its perimeter. However, in a confining theory, the action of the loop is instead proportional to its area. Since the area is proportional to the separation of the quark–antiquark pair, free quarks are suppressed. Mesons are allowed in such a picture, since a loop containing another loop with the opposite orientation has only a small area between the two loops. https://en.wikipedia.org/wiki/Color_confinement

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Examples

Example1

Example2:

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