Rotating Wilson loops and open strings in AdS3

TL;DR

This paper explores classical open string solutions in AdS3 related to Wilson loops and quark-antiquark pairs, utilizing Pohlmeyer reduction to connect equations to sinh-Gordon and Liouville equations, revealing new solutions and behaviors.

Contribution

It introduces a comprehensive analysis of open string solutions in AdS3 using Pohlmeyer reduction, including new solutions expressed via Riemann theta functions and a detailed study of rotating strings.

Findings

Derived new classical string solutions in AdS3.

Connected string equations to sinh-Gordon and Liouville equations.

Identified behaviors of rotating strings based on angular velocity.

Abstract

The AdS/CFT correspondence relates N=4 super Yang-Mills on S3 to type IIB string theory on AdS5xS5. In this context, a quark/anti-quark pair moving on an S1 inside S3 following prescribed trajectories is dual to an open string ending on the boundary of AdS3. In this paper we study the corresponding classical string solutions. The Pohlmeyer reduction reduces the equations of motion to a generalized sinh-Gordon equation. This equation includes, as particular cases, the Liouville equation as well as the sinh/cosh-Gordon equations. We study generic solutions of the Liouville equation and finite gap solutions of the sinh/cosh-Gordon ones. The latter ones are written in terms of Riemann theta functions. The corresponding string solutions are reconstructed giving new solutions and a broad understanding of open strings moving in AdS3. As a further example, the simple case of a rigidly rotating string is shown to exhibit these three behaviors depending on a simple relation between its angular velocity and the angular separation between its endpoints.