  We use the AdS/CFT correspondence to study the thermodynamics of massive N=2
supersymmetric hypermultiplet flavor fields coupled to N=4 supersymmetric
SU(Nc) Yang-Mills theory, formulated on curved four-manifolds, in the limits of
large Nc and large 't Hooft coupling. The gravitational duals are probe
D-branes in global thermal AdS. These D-branes may undergo a topology-changing
transition in the bulk. The D-brane embeddings near the point of the topology
change exhibit a scaling symmetry. The associated scaling exponents can be
either real- or complex-valued. Which regime applies depends on the
dimensionality of a collapsing submanifold in the critical embedding. When the
scaling exponents are complex-valued, a first-order transition associated with
the flavor fields appears in the dual field theory. Real scaling exponents are
expected to be associated with a continuous transition in the dual field
theory. For one example with real exponents, the D7-brane, we study the
transition in detail. We find two field theory observables that diverge at the
critical point, and we compute the associated critical exponents. We also
present analytic and numerical evidence that the transition expresses itself in
the meson spectrum as a non-analyticity at the critical point. We argue that
the transition we study is a true phase transition only when the 't Hooft
coupling is strictly infinite.
