Wilson loop operators  in Yang–Mills theories are non-local gauge invariant operators
To understand the prescription in [367, 433], one must first introduce massive quarks in the theory. This is achieved by breaking the original gauge symmetry of the original SYM according to
In this set-up, the massive W-boson interacts with the gauge fields, including the scalar adjoint fields , leading to the insertion of the operator
The proposal made in [367, 433] to compute the expectation value of Eq. (432) was5 and lying along on S5. Notice that a quantum mechanical calculation at strong coupling reduces to determining a minimal worldsheet surface in AdS5, i.e., solving the worldsheet equations of motion with appropriate boundary conditions, and then solving for the worldsheet energy as a function of the separation between the quark-antiquark. After subtracting the regularised mass of the W-boson one obtains the quark-antiquark potential energy
If one considers multiply-wrapped Wilson loops, the many coincident strings will suffer from self-interactions. This may suggest that a more appropriate description of the system is in terms of a D3-brane with non-trivial world volume electric flux accounting for the fundamental strings. This is the approach followed in , where it was shown that for linear and circular loops the D3-brane action agreed with the string worldsheet result at weak coupling, but captures all the higher-genus corrections at leading order in .
Living Rev. Relativity 15, (2012), 3
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