Correlators in higher spin AdS₃ holography from Wilson lines with loop corrections

We study the correlators of the 2d W_N minimal model in the semiclassical regime with large central charge from bulk viewpoint by utilizing open Wilson lines in sl(N) Chern-Simons gauge theory. We extend previous works for the tree level of bulk theory to incorporate loop corrections in this paper. We offer a way to regularize divergences associated with loop diagrams such that three point functions with two scalars and a higher spin current agree with the values fixed by the boundary W_N symmetry. With the prescription, we reproduce the conformal weight of the operator corresponding to a bulk scalar up to the two loop order for explicit examples with N=2,3.