Static strings in global AdS space and quark anti-quark potential

TL;DR

This paper studies the quark anti-quark potential at finite temperature in a compact space using static strings in global AdS space, revealing confining and deconfining phases linked to black hole solutions and Hawking-Page transition.

Contribution

It provides a detailed analysis of the quark anti-quark potential in global AdS space at finite temperature, connecting confinement/deconfinement to black hole solutions and Hawking-Page transition.

Findings

Potential is confining in AdS space and deconfining in the big black hole.

Small black hole shows confining potential but is unstable.

Results support the Hawking-Page transition as dual to confinement/deconfinement transition.

Abstract

We investigate the finite temperature quark anti-quark problem in a compact space $S^{n-1}\times S^1$ by considering static strings in global $AdS_{n+1}$ space with $n\ge 3$. For high temperatures we work in the black hole metric where two possible solutions show up : the big black hole and the small black hole. Using the AdS/CFT correspondence, we calculate the quark anti-quark potential (free energy) as a function of the distance. We show that this potential can be intrepeted as confining for the $AdS$ space and deconfining for the big black hole. We find for the small black hole a confining limit for the potential but this solution is instable following the Hawking-Page criteria. Our results for the free energy reinforce the Witten interpretation of the confinement/deconfinement transition as the dual of the well-known Hawking-Page transition.