Gravity Dual Corrections to the Heavy Quark Potential at Finite-Temperature

TL;DR

This paper computes finite-temperature corrections to heavy quark potentials in strongly coupled N=4 SYM plasma using gauge/gravity duality, revealing attractive potentials with Yukawa and Coulomb-like behaviors at different regimes.

Contribution

It provides the first detailed calculation of $1/N_c^2$ corrections to heavy quark potentials at finite temperature via supergravity mode exchanges in AdS/CFT.

Findings

All mode exchanges contribute attractively to the $Q\bar Q$ potential.

At large separations or high temperature, the potential is Yukawa-like, dominated by graviton exchange.

At small $rT$, the $Q\bar Q$ potential scales as $(1/r) \ln(1/rT)$.

Abstract

We apply gauge/gravity duality to compute $1/N^2_c$ corrections to the heavy quark potentials of a quark--anti-quark pair ($Q\bar Q$) and of a quark--quark pair ($QQ$) immersed into the strongly coupled N = 4 SYM plasma. On the gravity side these corrections come from the exchanges of supergravity modes between two string worldsheets stretching from the UV boundary of AdS space to the black hole horizon in the bulk and smeared over $S^5$. We find that the contributions to the $Q\bar Q$ potential coming from the exchanges of all of the relevant modes (such as dilaton, massive scalar, 2-form field, and graviton) are all attractive, leading to an attractive net $Q\bar Q$ potential. We show that at large separations $r$ and/or high-temperature $T$ the potential is of Yukawa-type, dominated by the graviton exchange, in agreement with earlier findings. On the other hand, at small-$r T$ the $Q\bar Q$ potential scales as $\sim (1/r) \ln (1/rT)$. In the case of $QQ$ potential the 2-form contribution changes sign and becomes repulsive: however, the net $QQ$ potential remains attractive. At large-$r T$ it is dominated by the graviton exchange, while at small-$r T$ the $QQ$ potential becomes Coulomb-like.