A Topology-Changing Phase Transition and the Dynamics of Flavour

In studying the dynamics of large N_c, SU(N_c) gauge theory at finite temperature with fundamental quark flavours 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 N_c D3-branes at finite temperature, AdS_5--Schwarzschild X S^5, probed by a D7-brane. The D7-brane has topology R^4 X S^3 X S^1 and allowed solutions correspond to either the S^3 or the S^1 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.