Conformal blocks from Wilson lines with loop corrections
Abstract:
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 offer a way to regularize divergences associated
with loop diagrams such that three point functions with two scalars and 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 two loop order. Moreover, we extend this prescription to conformal blocks
including loop corrections.