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

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–antiquark potential in a system with a 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–antiquark potential in QGP can be seen as a step towards a more exact theory that would incorporate time-varying thermal gradients. The effect of a static temperature gradient on the quark–antiquark potential is analyzed using a gravity dual model. A non-uniform black string metric is developed by perturbing the Schwarzschild metric, which allows us to incorporate the temperature gradient in the dual anti-de Sitter space. Finally, an expression for the quark–antiquark potential in the presence of a static temperature gradient is derived.