Topology-changing first order phase transition and the dynamics of flavor

In studying the dynamics of large Nc, SU(Nc) gauge theory at finite temperature with fundamental quark flavors in the quenched approximation, we observe a first order phase transition. A quark condensate forms at finite quark mass, and the value of the condensate varies smoothly with the quark mass for generic regions in parameter space. At a particular value of the quark mass, there is a finite discontinuity in the condensate's vacuum expectation value, corresponding to a first order phase transition. We study the gauge theory via its string dual formulation using the AdS/CFT conjecture, the string dual being the near-horizon geometry of Nc D3-branes at finite temperature, AdS₅-Schwarzschild×S⁵, probed by a D7-brane. The D7-brane has topology R⁴×S³×S¹ and allowed solutions correspond to either the S³ or the S¹ shrinking away in the interior of the geometry. The phase transition represents a jump between branches of solutions having these two distinct D-brane topologies. The transition also appears in the meson spectrum.