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

Abstract

In studying the dynamics of large ${N}_{c}$, $SU({N}_{c})$ 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 ${N}_{c}$ D3-branes at finite temperature, ${\mathrm{AdS}}_{5}\mathrm{\text{\ensuremath{-}}}\mathrm{\text{Schwarzschild}}\ifmmode\times\else\texttimes\fi{}{S}^{5}$, probed by a D7-brane. The D7-brane has topology ${\mathbb{R}}^{4}\ifmmode\times\else\texttimes\fi{}{S}^{3}\ifmmode\times\else\texttimes\fi{}{S}^{1}$ 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.