# Half-BPS Wilson loop and AdS$_2$/CFT$_1$

## TL;DR

This paper investigates correlation functions on the 1/2-BPS Wilson line in N=4 super Yang-Mills, using AdS/CFT to compute strong coupling limits and connecting results to 2D Yang-Mills theory.

## Contribution

It provides a detailed AdS/CFT analysis of four-point functions on the Wilson line and extracts strong coupling corrections to operator dimensions, linking to localization results.

## Key findings

- Computed tree-level AdS2 Witten diagrams for four-point functions.
- Extracted leading strong coupling anomalous dimensions.
- Matched results to 2D Yang-Mills predictions.

## Abstract

We study correlation functions of local operator insertions on the 1/2-BPS Wilson line in ${\cal N}=4$ super Yang-Mills theory. These correlation functions are constrained by the 1d superconformal symmetry preserved by the 1/2-BPS Wilson line and define a defect CFT$_1$ living on the line. At strong coupling, a set of elementary operator insertions with protected scaling dimensions correspond to fluctuations of the dual fundamental string in AdS$_5 \times S^5$ ending on the line at the boundary and can be thought of as light fields propagating on the AdS$_2$ worldsheet. We use AdS/CFT techniques to compute the tree-level AdS$_2$ Witten diagrams describing the strong coupling limit of the four-point functions of the dual operator insertions. Using the OPE, we also extract the leading strong coupling corrections to the anomalous dimensions of the "two-particle" operators built out of elementary excitations. In the case of the circular Wilson loop, we match our results for the 4-point functions of a special type of scalar insertions to the prediction of localization to 2d Yang-Mills theory.