# Note on generating functions and connected correlators of 1/2-BPS Wilson loops in $\mathcal{N}=4$ SYM theory

## TL;DR

This paper expresses generating functions for Wilson loops in $ ext{N}=4$ SYM using connected correlators and representation theory, confirming recent observations and providing new calculations of correlators at leading order.

## Contribution

It introduces a novel expression for generating functions of Wilson loops in terms of connected correlators, leveraging symmetric group representation theory, and confirms recent findings by Okuyama.

## Key findings

- Proof of the relation between generating functions and connected correlators
- New calculation of the connected 2-point correlator at leading order in 1/N
- Validation of recent observations by Okuyama

## Abstract

The generating functions for the Wilson loops in the symmetric and antisymmetric representations of the gauge group $U(N)$ are expressed in terms of the connected correlators of multiply-wound Wilson loops, using ingredients from the representation theory of the symmetric group. This provides a proof of a recent observation by Okuyama. As a by-product, we present a new calculation of the connected 2-point correlator of multiply-wound Wilson loops at leading order in $1/N$.