Heavy quark potential at finite temperature from gauge/string duality

Abstract

A static string in an AdS Schwarzschild space is dual to a heavy quark anti-quark pair in a gauge theory at high temperature. This space is non confining in the sense that the energy is finite for infinite quark anti-quark separation. We introduce an infrared cut off in this space and calculate the corresponding string energy. We find a deconfining phase transition at a critical temperature T_C. Above T_C the string tension vanishes representing the deconfined phase. Below T_C we find a linear confining behavior for large quark anti-quark separation. This simple phenomenological model leads to the appropriate zero temperature limit, corresponding to the Cornell potential and also describes a thermal deconfining phase transition. However the temperature corrections to the string tension do not recover the expected results for low temperatures.

Revision: V.3: Text improved, typos corrected, results unchanged, references added. We included a comparision between the low temperature corrections to the string tension in our model and the expected results for QCD. V.4: In this version we emphasize that our model is not appropriate for low temperatures. One more reference added

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