The Hagedorn transition, deconfinement and the AdS/CFT correspondence

A connection between the Hagedorn transition in string theory and the decon finement transition in (nonsupersymmetric) Yang-Mills theory is made using the AdS/CFT correspondence. We modify the model of zero temperature QCD pro posed by Witten by compactifying an additional space-time coordinate with s upersymmetry breaking boundary conditions thus introducing a finite tempera ture in the boundary theory. There is a Hagedorn-like transition associated with winding modes around this coordinate, which signals a topology changi ng phase transition to a new AdS/Schwarzschild black hole where this coordi nate is the time coordinate. In the boundary gauge theory time-like Wilson loops acquire an expectation value above this temperature.