Effect of temperature gradient on heavy quark anti-quark potential using gravity dual model

TL;DR

This paper extends the holographic approach to model the effect of static temperature gradients on the quark-antiquark potential in a QCD medium, using a gravity dual with a perturbed black string metric.

Contribution

It introduces a method to incorporate static thermal gradients into the holographic model of quark-antiquark potential via a perturbed black string metric.

Findings

Derived an expression for the quark-antiquark potential with a static temperature gradient.

Developed a non-uniform black string metric to model thermal gradients in the dual gravity theory.

Extended the Euclidean space approach to include static thermal gradients in QCD-like systems.

Abstract

Thermal systems have traditionally been modeled via Euclideanized space by analytical continuation of time to an imaginary time. We extend the concept to static thermal gradients by recasting the temperature variation as a variation in the Euclidean metric. We apply this prescription to determine the Quark anti-Quark potential in a system with thermal gradient. A naturally occurring QCD medium with thermal gradients is a Quark Gluon Plasma (QGP). However, the QGP evolves in time. Hence, we use a quasi-stationary approximation, which is applicable only if the rate of time evolution is slow. The application of our proposal to a Quark anti-Quark potential in QGP can be seen as a step towards a more exact theory which would incorporate time varying thermal gradients. The effect of a static temperature gradient on the Quark anti-Quark potential is analyzed using a gravity dual model. A non-uniform black string metric is developed, by perturbing the Schwarzchild metric, which allows to incorporate the temperature gradient in the dual AdS space. Finally, an expression for the Quark anti-Quark potential, in the presence of a static temperature gradient, is derived.