Wilson loops stability in the gauge/string correspondence

TL;DR

This paper investigates the stability of classical string solutions used to calculate quark potential energies in various gravity duals, revealing instabilities linked to the shape of the string embedding and discussing implications for gauge/string correspondence.

Contribution

It provides a detailed analysis of string stability in different gravity backgrounds, clarifies the role of diffeomorphism fixing, and explores implications for 't Hooft loops in non-conformal settings.

Findings

Instabilities occur for solutions with positive $L'(r_0)$.

Numerical analysis confirms the presence of linear fluctuation instabilities.

Discussion includes the interpretation of quark mass subtraction in confining backgrounds.

Abstract

We study the stability of some classical string worldsheet solutions employed for computing the potential energy between two static fundamental quarks in confining and non-confining gravity duals. We discuss the fixing of the diffeomorphism invariance of the string action, its relation with the fluctuation orientation and the interpretation of the quark mass substraction worldsheet needed for computing the potential energy in smooth (confining) gravity background. We consider various dual gravity backgrounds and show by a numerical analysis the existence of instabilities under linear fluctuations for classical string embedding solutions having positive length function derivative $L'(r_0)>0$. Finally we make a brief discussion of 't Hooft loops in non-conformal backgrounds.