Probing the Strong Coupling Limit of Large N SYM on Curved Backgrounds

According to the AdS/CFT correspondence, the strong coupling limit of largeN N =4 supersymmetric gauge theory at finite temperature is described by asymptotically anti de Sitter black holes. These black holes exist with planar, spherical and hyperbolic horizon geometries. We concentrate on the hyperbolic and spherical cases and probe the associated gauge theories with D3-branes and Wilson loops. The D3-brane probe reproduces the coupling of the scalars in the gauge theory to the background geometry and we find thermal stabilization in the hyperbolic case. We investigate the vacuum expectation value of Wilson loops with particular emphasis on the screening length at finite temperature. Somehow contrary to what one expects, we find that the thermal phase transition of the theory on the sphere is not related to screening phenomena.