Precision Test of Gauge-Gravity Duality with Flavor.

We put AdS/CFT dualities involving probe branes to a precision test. On the holographic side we use a new class of supersymmetric D7-brane embeddings into AdS(5)×S(5), which allow us to describe N=4 super Yang-Mills theory coupled to massive N=2 supersymmetric flavors on S(4). With these embeddings we can compare holographic results to a field theory analysis of the free energy using supersymmetric localization. Localization allows us to get results at strong coupling, and hence to compare in detail to AdS/CFT. We find analytically matching results: a phase transition at the same critical mass in both calculations and matching free energies up to a scheme-dependent constant in both phases.