Static strings in global AdS space and quark anti-quark potential
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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.
8 pages, 8 figures. V3 with a new discussion of the relation between the Wilson loop considered in the article and the Polyakov loops. New figures and a correction of figure 1. Accepted for publication in PRD
8 pages, 8 figures. V3 with a new discussion of the relation between the Wilson loop considered in the article and the Polyakov loops. New figures and a correction of figure 1. Accepted for publication in PRD