# The Wilson loop CFT: Insertion dimensions and structure constants from wavy lines

## TL;DR

This paper investigates operator insertions into the 1/2 BPS Wilson loop in N=4 SYM, calculating key CFT data such as two-point coefficients, anomalous dimensions, and structure constants, revealing their relation to line deformations.

## Contribution

It provides the first calculations of operator insertion data for the Wilson loop in N=4 SYM and clarifies the connection between line deformations and CFT operator data.

## Key findings

- Calculated two-point coefficients, anomalous dimensions, and structure constants for low-dimension insertions.
- Linked line deformations to operator insertions and their CFT data.
- Utilized known Wilson loop expectation values to derive new operator information.

## Abstract

We study operator insertions into the $1/2$ BPS Wilson loop in ${\cal N}=4$ SYM theory and determine their two-point coefficients, anomalous dimensions and structure constants. The calculation is done for the first few lowest dimension insertions and relies on known results for the expectation value of a smooth Wilson loop. In addition to the particular coefficients that we calculate, our study elucidates the connection between deformations of the line and operator insertions and between the vacuum expectation value of the line and the CFT data of the insertions.