# Double-helix Wilson loops: case of two angular momenta

## TL;DR

This paper analyzes double-helix Wilson loops with two angular momenta on S3, using integrable systems to compute their energy and angular momenta, extending previous models with a new multi-angular momentum case.

## Contribution

It introduces a string solution for double-helix Wilson loops with two angular momenta on S3, utilizing the Neumann-Rosochatius system for analysis, and explores the special case of a single angular momentum.

## Key findings

- Derived the string solution for double-helix Wilson loops with two angular momenta.
- Computed energy and angular momenta using the Neumann-Rosochatius system.
- Connected the single angular momentum case to analytic continuations of rotating strings in N=4 SYM.

## Abstract

Recently, Wilson loops with the shape of a double helix have played an important role in studying large spin operators in gauge theories. They correspond to a quark and an anti-quark moving in circles on an S3 (and therefore each of them describes a helix in RxS3). In this paper we consider the case where the particles have two angular momenta on the S3. The string solution corresponding to such Wilson loop can be found using the relation to the Neumann-Rosochatius system allowing the computation of the energy and angular momenta of the configuration. The particular case of only one angular momentum is also considered. It can be thought as an analytic continuation of the rotating strings which are dual to operators in the SL(2) sector of N=4 SYM.