The functional form of open Wilson lines in gauge theories coupled to matter

The open Wilson lines are gauge-invariant operators made with a gauge transporter along an open path saturated at the end-points with matter fields. Here it is shown that numerical experiments on 3D Z2 Higgs model provide useful guidance in addressing the problem of the functional form of their vacuum expectation values. It turns out they satisfy, as long as their size does not exceed the string breaking scale, a remarkable factorization, related to finite-size scaling of the Fredenhagen-Marcu order parameter. This leads to conjecture a decay area law, like ordinary Wilson loops, with the difference that the boundary conditions of the confining string world-sheet are fixed along the path of the gauge transporter whereas are free on the straight line joining the two end-points. A consistency condition fixes uniquely the contribution of the free boundary, which turns out to be proportional to the string-breaking scale. Universal shape effects produced by quantum string fluctuations are also studied.