Abstract
We investigate the finite temperature quark antiquark problem in a compact space ${S}^{n\ensuremath{-}1}\ifmmode\times\else\texttimes\fi{}{S}^{1}$ by considering static strings in global ${\mathrm{AdS}}_{n+1}$ space with $n\ensuremath{\ge}3$. 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 antiquark potential (free energy) as a function of the distance. We show that this potential can be intrepeted as confining for the anti-de Sitter (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.
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