Correlators in higher spin AdS_3 holography from Wilson lines with loop corrections

TL;DR

This paper advances the understanding of 2d W_N minimal model correlators in the semiclassical regime by incorporating loop corrections in the bulk via Wilson lines, aligning bulk calculations with boundary symmetry constraints.

Contribution

It introduces a regularization method for loop divergences in Wilson line calculations, enabling accurate two-loop order conformal weight computations for scalar operators.

Findings

Reproduces boundary conformal weights up to two loops for N=2,3

Provides a regularization scheme for loop divergences in Wilson line computations

Extends previous tree-level bulk calculations to include 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 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.