Probing the strong coupling limit of large N SYM on curved backgrounds

According to the AdS/CFT correspondence, the strong coupling limit of large N N = 4 supersymmetric gauge theory at finite temperature is described by asymptotically anti de Sitter black holes. These black holes exist with pla nar, spherical and hyperbolic horizon geometries. We concentrate on the hyp erbolic 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 expectatio n value of Wilson loops with particular emphasis on the screening length at finite temperature. We find that the thermal phase transition of the theor y on the sphere is not related to screening phenomena.